An Analysis of the Kinetic Energy in the Basket to Handstand on Parallel Bars: A Case Study of an Elite Gymnast

Abstract

(1) Background: This study aimed to examine the differences in the kinetic energy of the body’s center of mass between successful and unsuccessful attempts at transitioning from a basket to a handstand on the parallel bars. Special attention was given to the analysis of kinetic energy as a key factor in the efficient execution of this complex element. (2) Methods: The sample consisted of 10 successful and 10 unsuccessful attempts performed by an elite gymnast (a multiple-medalist in World and European Championships). All attempts and kinematic data were recorded and analyzed using high-frequency cameras (300 Hz) and the Ariel Performance 3D video system, respectively. Successful and unsuccessful performances were compared using a paired-sample t-test. (3) Results: Significant differences in kinetic energy were observed in the first part of the anti-gravitational phase of movement between successful and unsuccessful attempts. Successful attempts demonstrated a more favorable position at the beginning of this phase, allowing better utilization of accumulated kinetic energy—a higher position of the feet and hips, and a smaller shoulder joint angle at the moment the shoulder passed through the lower vertical. (4) Conclusions: Successful attempts in gymnastics are characterized by better biomechanical optimization and efficient kinetic energy use, achieved through an earlier entry into the second phase of movement with optimal body positioning, leading to greater peripheral and angular velocities crucial for performance.

Full text

Academic Editors: Sime Versic and
Nikola Foretic
Received: 30 December 2024
Revised: 22 January 2025
Accepted: 23 January 2025
Published: 25 January 2025
Citation: Veliˇckovi´c, S.; Ðor ¯
devi´c, D.;
Veliˇckovi´c, P.; Možnik, M.; Kolar, E.;
Stoica, C.-E.; Cristut
,ă, A.-M.; Voinea,
N.-L.; Vulpe, A.-M.; Bubanj, S.; et al.
An Analysis of the Kinetic Energy in
the Basket to Handstand on Parallel
Bars: A Case Study of an Elite
Gymnast. Life 2025,15, 172. https://
doi.org/10.3390/life15020172
Copyright: © 2025 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license
(https://creativecommons.org/
licenses/by/4.0/).
Case Report
An Analysis of the Kinetic Energy in the Basket to Handstand on
Parallel Bars: A Case Study of an Elite Gymnast
Saša Veliˇckovi´c
1
, Dušan Ðor ¯
devi´c
1
, Petar Veliˇckovi´c
1
, Marijo Možnik
2
, Edvard Kolar
3
, Cristina-Elena Stoica
4
,
Alina-Mihaela Cristu
t
,
ă
4
, Nicolae-Lucian Voinea
4
, Ana-Maria Vulpe
4
, Saša Bubanj
1,
* , Dušan Stankovi´c
1
,
Bojan Bjelica 5, Nikola Aksovi´c 6and Tatiana Dobrescu 4, *
1Faculty of Sport and Physical Education, University of Niš, 18000 Niš, Serbia; v.sale70@gmail.com (S.V.);
dusandjordjevic1995@gmail.com (D.Ð.); gimnastika1997@gmail.com (P.V.); dukislavujac@gmail.com (D.S.)
2Faculty of Kinesiology, University of Zagreb, 10000 Zagreb, Croatia; marijo.moznik@kif.unizg.hr
3Science and Research Centre Koper, 6600 Koper, Slovenia; edvard.kolar@zrs-kp.si
4Department of Physical Education and Sport Performance, Vasile Alecsandri University, 600115 Bacau,
Romania; cristina.popa@ub.ro (C.-E.S.); cristuta.alina@ub.ro (A.-M.C.); lucian.voinea@ub.ro (N.-L.V.);
zaharia.ana@ub.ro (A.-M.V.)
5
Faculty of Sport and Physical Education, University of Priština, Kosovska Mitrovica, 38218 Leposavi´c, Serbia;
vipbjelica@gmail.com
6Faculty of Physical Education and Sports, University of East Sarajevo, 71126 Lukavica,
Bosnia and Herzegovina; kokir87np@gmail.com
*Correspondence: bubanjsale@gmail.com (S.B.); tatiana.dobrescu@ub.ro (T.D.);
Tel.: +381-18-510900 (ext. 201) (S.B.); +40-234-542411 (T.D.)
Abstract: (1) Background: This study aimed to examine the differences in the kinetic
energy of the body’s center of mass between successful and unsuccessful attempts at
transitioning from a basket to a handstand on the parallel bars. Special attention was
given to the analysis of kinetic energy as a key factor in the efficient execution of this
complex element. (2) Methods: The sample consisted of 10 successful and 10 unsuccessful
attempts performed by an elite gymnast (a multiple-medalist in World and European
Championships). All attempts and kinematic data were recorded and analyzed using
high-frequency cameras (300 Hz) and the Ariel Performance 3D video system, respectively.
Successful and unsuccessful performances were compared using a paired-sample t-test.
(3) Results: Significant differences in kinetic energy were observed in the first part of
the anti-gravitational phase of movement between successful and unsuccessful attempts.
Successful attempts demonstrated a more favorable position at the beginning of this phase,
allowing better utilization of accumulated kinetic energy—a higher position of the feet and
hips, and a smaller shoulder joint angle at the moment the shoulder passed through the
lower vertical. (4) Conclusions: Successful attempts in gymnastics are characterized by
better biomechanical optimization and efficient kinetic energy use, achieved through an
earlier entry into the second phase of movement with optimal body positioning, leading to
greater peripheral and angular velocities crucial for performance.
Keywords: kinetic energy; gymnastics; kinematic analysis; parallel bars; biomechanics
1. Introduction
The model of successful performance for competitors in gymnastics consists of highly
complex coordination elements and their precise execution. A gymnast will be more
successful if they perform the most advanced coordination elements, such as those of D, E,
F, G, and H difficulty levels [
1
] (FIG), in their routines with minimal technical and esthetic
errors [2].
Life 2025,15, 172 https://doi.org/10.3390/life15020172

Life 2025,15, 172 2 of 14
Therefore, examining the technique of these complex elements and the errors made
during their execution is a key challenge for research in gymnastics. A rational and
economical process for teaching and perfecting these elements requires detailed analysis,
particularly for aspects of the technique that are not easily accessible to the coach’s visual
inspection or the gymnast’s kinesthetic receptors. These hidden technical details can only be
revealed through biomechanical analysis, specifically through the analysis of
kinetic energy.
Research in the field of biomechanical movement analysis is becoming increasingly
common in gymnastics, particularly over the last few decades, with a significant increase
in the number of publications since 2015 [
3
]. This trend reflects a continuous growth of
interest in biomechanical research in gymnastics, emphasizing the importance of such
analyses for optimizing performance and providing information to enable more rational
and efficient training, as well as the acquisition of complex movements [
4
,
5
]. Furthermore,
novel research is needed to identify and develop more effective strategies for enhancing
gymnast performance. Kinematic analysis plays a crucial role in understanding and
improving movement execution techniques across various sports disciplines, particularly
in gymnastics, where precision and control are of utmost importance [
6
]. However, while
kinematics is well-studied, the study of the role of kinetic and potential energy in sports,
particularly in gymnastics, is still a relatively new topic.
Recent research has focused on various aspects of kinetic energy in sports. For example,
Hoareau and associates [
7
] investigated the available sources of kinetic energy in the human
body during sports activities, focusing on its potential to be converted into electrical energy
using piezoelectric harvesters. This research underscores the importance of kinetic energy
in developing wearable sensors for monitoring sports performance. Wasserberger and
associates [
8
] analyzed the generation, absorption, and transfer of energy in the shoulder
and elbow joints of young baseball pitchers, exploring the relationship between these energy
measures and throwing velocity. Their findings highlight the importance of energy transfer
in achieving high throwing velocities while reducing the risk of injury. Understanding
energy transfer through the kinetic chain is crucial not only in gymnastics but also in
other sports. These findings can be viewed as analogous to energy transfer in complex
gymnastics elements, where the efficient use of kinetic energy can significantly impact
performance and reduce the risk of injury. Similarly, Priest and associates [
9
] focused on
evaluating athletic performance by considering athletes’ kinetic energy, which includes
velocity and body mass. Thus, kinetic energy, which accounts for both velocity and mass,
is a critical factor in assessing sports performance.
Furthermore, research by Jones and associates [10] demonstrated how kinetic energy
could be used to evaluate training effects and compare athletes and teams. Their work em-
ployed the “run-shuttle” test with a laser timer to measure time, velocity, and kinetic energy,
providing detailed insights into athlete performance across various sports (
e.g., American
football, soccer, basketball, and athletics). This approach can be compared with similar
analyses in gymnastics, where kinetic energy plays a crucial role in the execution technique
and achieving optimal performance. Regarding previously published studies in gymnastics,
Schärer and associates [
11
] analyzed differences in kinetic energy between Tsukahara and
Yurchenko vaults using 3D motion capture technology. Their findings revealed that the
Tsukahara vault is characterized by greater translational kinetic energy (TKE), whereas the
Yurchenko vault has greater angular kinetic energy (AKE). For more complex vaults, 5.9%
more AKE is required for each additional 180
◦
turn. This knowledge helps coaches assess
athletes’ potential and direct training toward appropriate physical and technical aspects of
the vault.

Life 2025,15, 172 3 of 14
Further research would provide deeper insights into how kinetic energy can be utilized
and analyzed in sports, contributing to a better understanding of the technical aspects
of performance. In gymnastics, a detailed understanding of biomechanical differences is
essential for optimizing execution techniques and improving performance through targeted
training processes.
This study aimed to examine the differences in the kinetic energy of the body’s center
of mass between successful and unsuccessful attempts at transitioning from a basket to
a handstand on the parallel bars, performed by an elite gymnast. Special attention has
been given to kinetic energy analysis as a key factor in the efficient execution of this
complex element.
2. Materials and Methods
2.1. Participant
The sample consisted of one elite gymnast (age: 26; body height: 165 cm; body mass:
63 kg). The inclusion criteria required that the participant be male and a medalist at
the World or European Championships. The exclusion criteria included current injuries
affecting performance and a lack of consent for participation in the study. The Gymnastics
Federation of Serbia approved all experimental procedures on 27 October 2023 (approval
No. 11-485/23) in accordance with the Helsinki Declaration for studies on humans [12].
2.2. Study Design
This study employed a case study design. One elite male gymnast was recruited to
analyze kinetic energy between successful and unsuccessful attempts during the basket
to handstand on parallel bars gymnastic element. The authors examined the total kinetic
energy (KEtotal), kinetic energy of translational motion (KEtrans), and kinetic energy of
rotational motion (KErot).
2.3. Procedures
The gymnast performed 45 attempts of the basket to handstand on parallel bars
(
Figure 1
) under experimental conditions, with varying levels of success. Out of
45 attempts
performed by the participant, 10 successful and 10 unsuccessful attempts were ana-
lyzed and graphically represented as the mean values. After each attempt, a 60 s break
would follow. All repetitions were recorded using two high-frequency CASIO DIGITAL
CAMERA EX-F1 devices (Casio Computer Co., Ltd., Tokyo, Japan), which were inter-
connected and synchronized. The cameras operated at a frequency of 300 Hz with a
resolution of 720
×
576 pixels. Simultaneously, three internationally accredited judges
(
FIG-BREVET
) evaluated the success of each attempt using the current “E” panel scor-
ing system. The assessment focused on both technical execution, such as proper body
alignment, smooth transitions, controlled movements, and maintaining straight arms,
as well as esthetic elements, including pointed toes, fluidity, and overall presentation.
Deductions were applied for noticeable deviations, loss of balance, or incomplete exten-
sion in the handstand position [
13
]. The final classification of attempts as successful or
unsuccessful was determined based on the judges’ scores, adhering strictly to the FIG
evaluation criteria.

Life 2025,15, 172 4 of 14
Life 2025, 15, x FOR PEER REVIEW 4 of 15
Figure 1. Basket to handstand on the parallel bars through positions (1–10) and phases [14].
To determine the kinematic parameters of the selected aempts, the Ariel Perfor-
mance 3D analysis system (APAS, version 13.2.1) was used for kinematic analysis. The
Center of Mass in the APAS is calculated using a segmental analysis approach, where each
body segment’s mass and position are considered based on anthropometric data. This
method integrates the positional data of body landmarks captured during motion analysis
[15]. The calibration of the space was performed using two reference frames positioned in
the middle of the parallel bars, allowing for precise digitalization of the gymnast’s posi-
tion in each phase of the element (Figure 2). All aempts were recorded at a frequency of
300 Hz.
Figure 2. Calibration space [16].
The digitization of the athlete’s body model, consisting of 15 segments, was defined
using 16 reference points [17]. The validity and reliability of the model were confirmed by
[18]. As presented elsewhere [15], the 15-segment model included the head, shoulder
width, left and right upper arms, left and right forearms, left and right sides of the torso,
hip width, left and right thighs, left and right lower legs, and left and right feet (Figure
3a). The verification of anatomical reference positions was assessed electronically by the
same rater. Two video cameras were able to record and quantitatively determine the
movement of each body component. By projecting each frame of the video onto the mon-
itor and locating the pointer, each position of the ploed reference point was assigned a
numerical value from the selected coordinate system. After digitization, the APAS
Figure 1. Basket to handstand on the parallel bars through positions (1–10) and phases [14].
To determine the kinematic parameters of the selected attempts, the Ariel Performance
3D analysis system (APAS, version 13.2.1) was used for kinematic analysis. The Center
of Mass in the APAS is calculated using a segmental analysis approach, where each body
segment’s mass and position are considered based on anthropometric data. This method
integrates the positional data of body landmarks captured during motion analysis [
15
].
The calibration of the space was performed using two reference frames positioned in the
middle of the parallel bars, allowing for precise digitalization of the gymnast’s position in
each phase of the element (Figure 2). All attempts were recorded at a frequency of 300 Hz.
Life 2025, 15, x FOR PEER REVIEW 4 of 15
Figure 1. Basket to handstand on the parallel bars through positions (1–10) and phases [14].
To determine the kinematic parameters of the selected aempts, the Ariel Perfor-
mance 3D analysis system (APAS, version 13.2.1) was used for kinematic analysis. The
Center of Mass in the APAS i s calculated using a segmental analysis approach, where each
body segment’s mass and position are considered based on anthropometric data. This
method integrates the positional data of body landmarks captured during motion analysis
[15]. The calibration of the space was performed using two reference frames positioned in
the middle of the parallel bars, allowing for precise digitalization of the gymnast’s posi-
tion in each phase of the element (Figure 2). All aempts were recorded at a frequency of
300 Hz.
Figure 2. Calibration space [16].
The digitization of the athlete’s body model, consisting of 15 segments, was defined
using 16 reference points [17]. The validity and reliability of the model were confirmed by
[18]. As presented elsewhere [15], the 15-segment model included the head, shoulder
width, left and right upper arms, left and right forearms, left and right sides of the torso,
hip width, left and right thighs, left and right lower legs, and left and right feet (Figure
3a). The verification of anatomical reference positions was assessed electronically by the
same rater. Two video cameras were able to record and quantitatively determine the
movement of each body component. By projecting each frame of the video onto the mon-
itor and locating the pointer, each position of the ploed reference point was assigned a
numerical value from the selected coordinate system. After digitization, the APAS
Figure 2. Calibration space [16].
The digitization of the athlete’s body model, consisting of 15 segments, was defined
using 16 reference points [
17
]. The validity and reliability of the model were confirmed
by [
18
]. As presented elsewhere [
15
], the 15-segment model included the head, shoulder
width, left and right upper arms, left and right forearms, left and right sides of the torso, hip
width, left and right thighs, left and right lower legs, and left and right feet (Figure 3a). The
verification of anatomical reference positions was assessed electronically by the same rater.
Two video cameras were able to record and quantitatively determine the movement of each
body component. By projecting each frame of the video onto the monitor and locating the
pointer, each position of the plotted reference point was assigned a numerical value from

Life 2025,15, 172 5 of 14
the selected coordinate system. After digitization, the APAS automatically calculated the
trajectory of the body’s center of mass along the x, y, and z axes for each selected frame, as
well. Since the executed element has characteristics of two-dimensional movement, only
the right side of the body was considered for further analysis (Figure 3b). Additionally, as
there was no significant movement along the medio-lateral (z) axis, values on the z-axis
were not included in the analysis. Kinograms were presented as a stick figures, which
represent simplified models of the human body and motion of the gymnast.
Life 2025, 15, x FOR PEER REVIEW 5 of 15
automatically calculated the trajectory of the body’s center of mass along the x, y, and z
axes for each selected frame, as well. Since the executed element has characteristics of two-
dimensional movement, only the right side of the body was considered for further analy-
sis (Figure 3b). Additionally, as there was no significant movement along the medio-lat-
eral (z) axis, values on the z-axis were not included in the analysis. Kinograms were pre-
sented as a stick figures, which represent simplified models of the human body and mo-
tion of the gymnast.
(a) (b)
Figure 3. Digitizing process in APAS: (a) 15-segment model and (b) stick figure model [15].
Following the digitization of each frame of the analyzed movement in APAS and the
subsequent automatic calculation of all the necessary kinematic parameters, the kinetic
energy was calculated. The formula used to calculate kinetic energy was as follows [19]:
KEtotal = KEtrans + KErot = ଵ
ଶ mv2 + ଵ
ଶ Iω2
Legend: KEtotal—total kinetic energy; KEtrans—kinetic energy of translational mo-
tion; KErot—kinetic energy of rotational motion; m—mass of the gymnast; v—velocity of
the center of mass in translational motion; I—moment of inertia of the gymnast; ω—an-
gular velocity of the center of mass/axis of rotation.
2.4. Statistical Analysis
The Kolmogorov–Smirnov test was used to assess the normality of the data distribu-
tion. To assess the difference between successful and unsuccessful aempts, a paired-sam-
ples t-test was used.
All statistical analyses were considered significant at p < 0.05. The percent difference
between means were also calculated (∆ (%)). For more sensitive analysis, an effect size (ES)
was calculated. The ES was presented as follows: d < 0.2—trivial effect; 0.2 ≤ d < 0.5—small
effect; 0.5 ≤ d < 0.8—medium effect; and d ≥ 0.8—large effect [20]. The data were analyzed
using the Statistical Package for Social Sciences (SPSS) software (v20.0, SPSS Inc., Chicago,
IL, USA).
3. Results
In the following text, the term “positions” refers to specific moments within a basket
to handstand technique. These positions mark critical points where significant
Figure 3. Digitizing process in APAS: (a) 15-segment model and (b) stick figure model [15].
Following the digitization of each frame of the analyzed movement in APAS and the
subsequent automatic calculation of all the necessary kinematic parameters, the kinetic
energy was calculated. The formula used to calculate kinetic energy was as follows [19]:
KEtotal =KEtrans +KErot =1
2mv2+1
2Iω2
Legend: KEtotal—total kinetic energy; KEtrans—kinetic energy of translational mo-
tion; KErot—kinetic energy of rotational motion; m—mass of the gymnast; v—velocity of
the center of mass in translational motion; I—moment of inertia of the gymnast;
ω
—angular
velocity of the center of mass/axis of rotation.
2.4. Statistical Analysis
The Kolmogorov–Smirnov test was used to assess the normality of the data distri-
bution. To assess the difference between successful and unsuccessful attempts, a paired-
samples t-test was used.
All statistical analyses were considered significant at p< 0.05. The percent difference
between means were also calculated (
∆
(%)). For more sensitive analysis, an effect size (ES)
was calculated. The ES was presented as follows: d < 0.2—trivial effect;
0.2 ≤d < 0.5—small
effect; 0.5
≤
d < 0.8—medium effect; and d
≥
0.8—large effect [
20
]. The data were analyzed
using the Statistical Package for Social Sciences (SPSS) software (v20.0, SPSS Inc., Chicago,
IL, USA).

Life 2025,15, 172 6 of 14
3. Results
In the following text, the term “positions” refers to specific moments within a basket to
handstand technique. These positions mark critical points where significant biomechanical
changes took place, such as alterations in the gymnast’s body posture, movement trajectory,
or kinetic energy.
The analyzed element was divided into two phases [
14
], the gravitational and anti-
gravitational phase. During the gravitational phase, the body’s center of mass moves in
the direction of gravitational force and accumulates kinetic energy. Specifically, this phase
includes the movement from a handstand swing (position 17) and further descent to a lifted
hang (position 53). During the anti-gravitational phase, the body’s center of mass moves
against the force of gravity during this phase, encompassing the transition from the lifted
hang (position 53) to position 70 and continuing into the handstand.
Notably, the entire body rotates around the grip axis (Figure 4), while additional
rotations occur within subsystems, the trunk–legs system rotates around the shoulder axis,
and the legs system rotates around the hip axis. The center of mass for the body was
automatically calculated for each selected frame using the APAS system.
Life 2025, 15, x FOR PEER REVIEW 6 of 15
biomechanical changes took place, such as alterations in the gymnast’s body posture,
movement trajectory, or kinetic energy.
The analyzed element was divided into two phases [14], the gravitational and anti-
gravitational phase. During the gravitational phase, the body’s center of mass moves in
the direction of gravitational force and accumulates kinetic energy. Specifically, this phase
includes the movement from a handstand swing (position 17) and further descent to a
lifted hang (position 53). During the anti-gravitational phase, the body’s center of mass
moves against the force of gravity during this phase, encompassing the transition from
the lifted hang (position 53) to position 70 and continuing into the handstand.
Notably, the entire body rotates around the grip axis (Figure 4), while additional ro-
tations occur within subsystems, the trunk–legs system rotates around the shoulder axis,
and the legs system rotates around the hip axis. The center of mass for the body was au-
tomatically calculated for each selected frame using the APAS system.
Figure 4. Trajectory of body’s center of mass in meters (m); Succ. A.—figure made using mean
values of successful aempts.
Figure 5a–c presents the average values of all calculated forms of kinetic energy
(translational, rotational, and total) for successful and unsuccessful aempts. Regarding
translational kinetic energy (Figure 5a), successful aempts demonstrate higher peaks
during the anti-gravitational phase, indicating greater momentum and more effective en-
ergy transfer. Successful aempts display smoother increases for rotational kinetic energy
(Figure 5b) and higher peaks during key transitions, reflecting beer coordination and
control of rotational movement. As for total kinetic energy (Figure 5c), successful aempts
consistently achieve greater values, especially in the anti-gravitational phase, emphasiz-
ing the importance of efficiently integrating translational and rotational energies for opti-
mal performance.
Figure 4. Trajectory of body’s center of mass in meters (m); Succ. Att.—figure made using mean
values of successful attempts.
Figure 5a–c presents the average values of all calculated forms of kinetic energy
(translational, rotational, and total) for successful and unsuccessful attempts. Regarding
translational kinetic energy (Figure 5a), successful attempts demonstrate higher peaks
during the anti-gravitational phase, indicating greater momentum and more effective
energy transfer. Successful attempts display smoother increases for rotational kinetic
energy (Figure 5b) and higher peaks during key transitions, reflecting better coordination
and control of rotational movement. As for total kinetic energy (Figure 5c), successful
attempts consistently achieve greater values, especially in the anti-gravitational phase,
emphasizing the importance of efficiently integrating translational and rotational energies
for optimal performance.
The kinetic energy does not increase steadily but instead fluctuates in a wave-like
pattern. The first significant drop in energy occurs at position 29 (Figure 6a), coinciding with
the shoulder point leaving the support surface and an increase in the shoulder joint angle
due to anteflexion. This decrease is likely deliberate, as the gymnast consciously decelerates

Life 2025,15, 172 7 of 14
to prepare more precisely for the subsequent phase. Once the tips of the feet enter the
anti-gravitational phase at position 34, dynamic hip joint flexion intensifies, leading to a
renewed increase in kinetic energy.
Life 2025, 15, x FOR PEER REVIEW 7 of 15
(a) (b)
(c)
Figure 5. The kinetic energy of the body’s center of mass during successful and unsuccessful at-
tempts, expressed as average values in Joules (J): (a) translational kinetic energy, highlighting the
movement of the body’s center of mass along a linear path; (b) rotational kinetic energy, illustrating
the rotational motion of the body’s center of mass around its axis; (c) total kinetic energy, which is
the sum of translational and rotational kinetic energies. The x-axis represents the positions and
phases of movement, divided into gravitational (1–53) and anti-gravitational (54–113) phases. The
vertical lines indicate key transition points, with visual markers of body positions during those
phases. Succ. A.—figure made using the mean values of successful aempts; Unsucc. A.—figure
made using the mean values of unsuccessful aempts.
The kinetic energy does not increase steadily but instead fluctuates in a wave-like
paern. The first significant drop in energy occurs at position 29 (Figure 6a), coinciding
with the shoulder point leaving the support surface and an increase in the shoulder joint
angle due to anteflexion. This decrease is likely deliberate, as the gymnast consciously
decelerates to prepare more precisely for the subsequent phase. Once the tips of the feet
enter the anti-gravitational phase at position 34, dynamic hip joint flexion intensifies, lead-
ing to a renewed increase in kinetic energy.
Figure 5. The kinetic energy of the body’s center of mass during successful and unsuccessful attempts,
expressed as average values in Joules (J): (a) translational kinetic energy, highlighting the movement
of the body’s center of mass along a linear path; (b) rotational kinetic energy, illustrating the rotational
motion of the body’s center of mass around its axis; (c) total kinetic energy, which is the sum of
translational and rotational kinetic energies. The x-axis represents the positions and phases of
movement, divided into gravitational (1–53) and anti-gravitational (54–113) phases. The vertical
lines indicate key transition points, with visual markers of body positions during those phases. Succ.
Att.—figure made using the mean values of successful attempts; Unsucc. Att.—figure made using
the mean values of unsuccessful attempts.
The second drop in kinetic energy begins after position 43 (Figure 6b), as the shoulder
point enters the second quadrant of its circular trajectory, moving below the bars. During
this phase, the tips of the feet start ascending, the hip point reaches the lowest point of the
gravitational phase, and the angular velocity of the hip joint decreases.
Kinetic energy continues to decline until the shoulder point transitions into the anti-
gravitational phase (position 53, the third quadrant of the shoulder point’s circular move-
ment). Between positions 50 and 53, while kinetic energy is still decreasing, retroflexion in
the shoulder joint begins, accompanied by maximum flexion in the hip joint.

Life 2025,15, 172 8 of 14
After position 53, as the hip point rises above the level of the shoulder point, kinetic
energy starts to increase again, initiating a phase of accelerated hip extension and shoulder
anteflexion, and maximum kinetic energy is achieved at position 62, driven by the continued
increase in the angular velocity of hip extension and shoulder anteflexion. The energy is
partially maintained through the next two positions, at which point the center of mass and
the hip point are positioned above the bars (Figure 7).
Life 2025, 15, x FOR PEER REVIEW 8 of 15
(a) (b)
Figure 6. Drops in kinetic energy: (a) the first drop occurs between positions 29 and 34, and (b) the
second drop occurs at position 43 and between positions 50 and 53. Succ. A.—figure made using
the mean values of successful aempts.
The second drop in kinetic energy begins after position 43 (Figure 6b), as the shoulder
point enters the second quadrant of its circular trajectory, moving below the bars. During
this phase, the tips of the feet start ascending, the hip point reaches the lowest point of the
gravitational phase, and the angular velocity of the hip joint decreases.
Kinetic energy continues to decline until the shoulder point transitions into the anti-
gravitational phase (position 53, the third quadrant of the shoulder point’s circular move-
ment). Between positions 50 and 53, while kinetic energy is still decreasing, retroflexion
in the shoulder joint begins, accompanied by maximum flexion in the hip joint.
After position 53, as the hip point rises above the level of the shoulder point, kinetic
energy starts to increase again, initiating a phase of accelerated hip extension and shoul-
der anteflexion, and maximum kinetic energy is achieved at position 62, driven by the
continued increase in the angular velocity of hip extension and shoulder anteflexion. The
energy is partially maintained through the next two positions, at which point the center
of mass and the hip point are positioned above the bars (Figure 7).
Figure 6. Drops in kinetic energy: (a) the first drop occurs between positions 29 and 34, and (b) the
second drop occurs at position 43 and between positions 50 and 53. Succ. Att.—figure made using
the mean values of successful attempts.
Life 2025, 15, x FOR PEER REVIEW 9 of 15
Figure 7. The body’s center of mass and body segments in position 62—kinetic energy at its highest
level; Succ. A.—figure made using the mean values of successful aempts.
Following position 65, as the tips of the feet aain maximum velocity and the hip
joint reaches its peak velocity, a sharp drop in kinetic energy occurs. The movement from
position 65 to 68 exemplifies the biomechanical principle of transferring kinetic energy
from the open end of the kinetic chain (feet) to the closed end (shoulder point) (Figure 8a).
In the final stages of the movement, a minor wave appears—a slight increase in ki-
netic energy between positions 71 and 80 (Figure 8b). This occurs during the laer part of
the non-support phase and the re-establishment of contact with the bars. After re-contact-
ing the bars, kinetic energy decreases steadily until the conclusion of the movement.
(a) (b)
Figure 7. The body’s center of mass and body segments in position 62—kinetic energy at its highest
level; Succ. Att.—figure made using the mean values of successful attempts.

Life 2025,15, 172 9 of 14
Following position 65, as the tips of the feet attain maximum velocity and the hip
joint reaches its peak velocity, a sharp drop in kinetic energy occurs. The movement from
position 65 to 68 exemplifies the biomechanical principle of transferring kinetic energy
from the open end of the kinetic chain (feet) to the closed end (shoulder point) (Figure 8a).
Life 2025, 15, x FOR PEER REVIEW 9 of 15
Figure 7. The body’s center of mass and body segments in position 62—kinetic energy at its highest
level; Succ. A.—figure made using the mean values of successful aempts.
Following position 65, as the tips of the feet aain maximum velocity and the hip
joint reaches its peak velocity, a sharp drop in kinetic energy occurs. The movement from
position 65 to 68 exemplifies the biomechanical principle of transferring kinetic energy
from the open end of the kinetic chain (feet) to the closed end (shoulder point) (Figure 8a).
In the final stages of the movement, a minor wave appears—a slight increase in ki-
netic energy between positions 71 and 80 (Figure 8b). This occurs during the laer part of
the non-support phase and the re-establishment of contact with the bars. After re-contact-
ing the bars, kinetic energy decreases steadily until the conclusion of the movement.
(a) (b)
Figure 8. The movement of the body’s center of mass in the x/y plane through positions: (a) 65–68—
beginning of the steep drop in kinetic energy and (b) 71–80—non-support phase; Succ. Att.—figure
made using mean values of successful attempts.
In the final stages of the movement, a minor wave appears—a slight increase in kinetic
energy between positions 71 and 80 (Figure 8b). This occurs during the latter part of the
non-support phase and the re-establishment of contact with the bars. After re-contacting
the bars, kinetic energy decreases steadily until the conclusion of the movement.
As shown in Table 1, translational kinetic energy exhibited a statistically significant
difference between successful and unsuccessful attempts from position 56 onward. The
average value of translational kinetic energy at position 56 was 338.640 J for successful
attempts, compared to 293.616 J for unsuccessful attempts, representing a difference of
45.024 J (15%) in favor of successful attempts. The effect size (ES) using Cohen’s d is 1.37,
indicating a large effect and a pronounced difference.
Table 1. Comparison of kinetic energy variables between successful and unsuccessful attempts.
Variable KP
Successful [J]
Unsuccessful [J] Diff [J] t-Test p∆(%) ES
KEtrans 56 338.640 293.616 45.024 2.412 0.03 15% 1.37 ***
KErot 57 218.593 186.177 32.416 2.222 0.04 17% 1.24 ***
KEtotal 57 596.541 508.694 87.847 2.636 0.02 17% 1.53 ***
Legend: KEtotal—total kinetic energy; KEtrans—kinetic energy of translational motion; KErot—kinetic energy of
rotational motion; KP—position where statistically significant difference begins; J—joules; Diff—numerical
difference between arithmetic means; t-Test—numerical value of t-test; p—statistical significance of t-test;
∆
(%)—percent difference between successful and unsuccessful performances; difference is very pronounced and
significant ***; ES—Effect Size.

Life 2025,15, 172 10 of 14
Rotational kinetic energy also displays a statistically significant difference starting from
position 57. Successful attempts show an average value of 218.593 J, while unsuccessful
attempts average 186.177 J, resulting in a difference of 32.416 J (17%). The ES is 1.24, again
indicating a large effect.
Total kinetic energy revealed a statistically significant difference at position 57, with
successful attempts averaging 596.541 J compared to 508.694 J for unsuccessful attempts.
This difference of 87.847 J (17%) highlights a very large effect size (ES = 1.53), underscoring
a pronounced distinction favoring successful attempts.
The t-test results confirmed statistically significant differences (p< 0.05) between
successful and unsuccessful attempts for translational, rotational, and total kinetic energy
from positions 56–57 onward (Figure 9). These findings support the conclusion that the
observed differences were not due to chance, with greater kinetic energy values consistently
associated with successful attempts.
Life 2025, 15, x FOR PEER REVIEW 11 of 15
(a) (b)
Figure 9. Aempts: (a) successful (green stick figures), and (b) unsuccessful (red stick figures), po-
sitions 56–70.
4. Discussion
The execution of complex gymnastics skills, like the basket to handstand, requires
the precise coordination of biomechanical factors and technical execution to achieve suc-
cessful performance. However, the factors that differentiate successful from unsuccessful
aempts in elite-level gymnastics are not fully understood, particularly regarding the role
of kinetic energy in movement efficiency and control. Identifying these differences is cru-
cial for optimizing training methods and refining techniques.
The aim of this study was to examine the differences in the kinetic energy of the
body’s center of mass between successful and unsuccessful aempts of the basket-to-
handstand on the parallel bars performed by an elite gymnast. The main findings of the
study revealed significant differences in kinetic energy between successful and unsuccess-
ful aempts, with large ES values for all analyzed variables. These findings can help iden-
tify key techniques and movement paerns that contribute to the success of gymnastics
elements.
The efficient use of kinetic energy is crucial for the successful execution of gymnastics
elements [21]. Recent studies suggest that biomechanical analyses can significantly con-
tribute to optimizing performance techniques, movement stability, efficiency, and preci-
sion, particularly in disciplines such as acrobatics and gymnastics [22,23]. These insights
can further support achieving beer results [24].
The study results highlight that differences in kinetic energy begin at the start of the
second phase of movement, the anti-gravitational phase, specifically during the sub-phase
of the lifted hang (Figure 9). Regarding trajectory differences, successful aempts were
characterized by greater and more consistent kinetic energy values.
Based on these findings, the following observations can be made:
A higher position of the feet and hips at the start of the anti-gravitational phase in
successful aempts may indicate beer biomechanical optimization of the movement, al-
lowing the gymnast to use gravitational force more effectively to generate kinetic energy.
Because of their initial height above the bars, the gymnast has a lot of potential energy at
Figure 9. Attempts: (a) successful (green stick figures), and (b) unsuccessful (red stick figures),
positions 56–70.
The large ES (Cohen’s d > 0.8) values observed for all kinetic energy variables indicate
that the differences are not only statistically significant but also practically meaningful,
highlighting their substantial impact on performance outcomes. Furthermore, the percent-
age differences between successful and unsuccessful attempts, ranging from 15% to 17%,
reinforce the importance of these kinetic parameters in determining success, as validated
by the t-test and effect size results.
4. Discussion
The execution of complex gymnastics skills, like the basket to handstand, requires the
precise coordination of biomechanical factors and technical execution to achieve successful
performance. However, the factors that differentiate successful from unsuccessful attempts

Life 2025,15, 172 11 of 14
in elite-level gymnastics are not fully understood, particularly regarding the role of kinetic
energy in movement efficiency and control. Identifying these differences is crucial for
optimizing training methods and refining techniques.
The aim of this study was to examine the differences in the kinetic energy of the body’s
center of mass between successful and unsuccessful attempts of the basket-to-handstand on
the parallel bars performed by an elite gymnast. The main findings of the study revealed
significant differences in kinetic energy between successful and unsuccessful attempts, with
large ES values for all analyzed variables. These findings can help identify key techniques
and movement patterns that contribute to the success of gymnastics elements.
The efficient use of kinetic energy is crucial for the successful execution of gymnastics
elements [
21
]. Recent studies suggest that biomechanical analyses can significantly con-
tribute to optimizing performance techniques, movement stability, efficiency, and precision,
particularly in disciplines such as acrobatics and gymnastics [
22
,
23
]. These insights can
further support achieving better results [24].
The study results highlight that differences in kinetic energy begin at the start of the
second phase of movement, the anti-gravitational phase, specifically during the sub-phase
of the lifted hang (Figure 9). Regarding trajectory differences, successful attempts were
characterized by greater and more consistent kinetic energy values.
Based on these findings, the following observations can be made:
A higher position of the feet and hips at the start of the anti-gravitational phase in
successful attempts may indicate better biomechanical optimization of the movement,
allowing the gymnast to use gravitational force more effectively to generate kinetic energy.
Because of their initial height above the bars, the gymnast has a lot of potential energy at
the lowest point of the “basket” posture. During the upward swing, this potential energy
which was obtained from the original downward swing is successfully converted into
kinetic energy. In order to gain enough height and velocity to return to the handstand
posture with ease, this energy conversion is essential.
Kinetic energy is directly influenced by velocity, as it is proportional to the square of
velocity. In artistic gymnastics velocity has an important role in successfully performing
elements [
25
]. Greater translational and rotational kinetic energy observed in successful
attempts indicates a greater peripheral velocity of body segments (feet, hips, and shoulders)
and increased angular velocities in hip extension and shoulder anteflexion, highlighting
the critical role of velocity in achieving optimal performance. This is in accordance with the
study of Gervais and Dunn [
26
], who showed that greater vertical velocity induces better
performance in the double back salto dismount on parallel bars.
Therefore, greater peripheral velocity values at the tips of the feet, hips, and shoulder
point, along with greater angular velocities of hip extension and shoulder anteflexion in
successful attempts, indicate better coordination and synchronization of movements. This
contributes to improved force transmission through the kinetic chain, enhancing overall
movement efficiency [27].
Earlier and faster opening of the kinetic chain: In successful attempts, the opening of
the kinetic chain begins earlier and faster due to a more favorable position when entering
the second phase (higher hips and feet, smaller shoulder joint angle). This suggests that
the gymnast is more successful in initiating and executing movements at critical moments,
enabling the more efficient use of accumulated kinetic energy.
Successful attempts demonstrate more proper use of accumulated energy during the
gravitational phase, allowing for better performance in the anti-gravitational phase. This
indicates that the gymnast has greater control over kinetic energy, optimizing its use to
achieve greater velocity and precision.

Life 2025,15, 172 12 of 14
Greater peripheral velocity values at the tips of the feet, hips, and shoulder point,
along with greater angular velocities of hip extension and shoulder anteflexion in suc-
cessful attempts, indicate better coordination and synchronization of movements. This
contributes to improved force transmission through the kinetic chain, enhancing overall
movement efficiency.
The results of this study can be directly applied to the training process by focusing
on the optimal use of kinetic energy in key movement phases. This includes introducing
specific exercises that simulate the transition from the gravitational to the anti-gravitational
phase, thereby improving movement efficiency and reducing the risk of injury. In practice,
essential pedagogical principles should be followed [28].
Similar to the findings of Wasserberger and associates [
8
], who demonstrated that
throwing velocity in young baseball pitchers largely depends on the efficient transfer of
energy between the shoulder and elbow, this study highlights that the efficient use of kinetic
energy is critical for the successful execution of gymnastics elements. Although handgrip
strength serves as a common link between baseball players and gymnasts [
29
], from a
practical standpoint, significant handgrip strength is crucial, primarily for performance
improvement. Additionally, it should not be overlooked that gymnasts perform elements
around stationary apparatus for extended periods [
29
–
32
]. Consequently, regarding its
contribution as a significant factor in parallel bar performance [
33
], our findings also
indicate that greater kinetic energy in key movement phases leads to improved performance,
consistent with the aforementioned studies.
Jones and associates [
10
] developed a method for evaluating the kinetic energy of
athletes using the “run-shuttle” test, which enabled a more precise identification of athlete
characteristics based on velocity and kinetic energy. Similarly, our analysis of kinetic
energy in gymnastics elements follows comparable principles, where greater kinetic energy
values are associated with more successful element execution. This confirms the universal
significance of kinetic energy as a key factor in assessing sports performance, whether
in dynamic sports like football or in sports with complex coordination demands such as
gymnastics. These findings can help enhance training programs to optimize and maximize
performance across a range of sports disciplines. The practical implications of these findings
can be applied in targeted training processes through specific exercises that simulate
transitions between movement phases, improving movement efficiency and reducing
injury risks.
This study is limited by its sample size, as it analyzed only one elite gymnast. Fu-
ture research should include a larger sample size to generalize the results. Additionally,
incorporating other complex elements and different apparatus could contribute to a more
comprehensive understanding of the role of kinetic energy in gymnastics.
5. Conclusions
Based on the analysis, we concluded that successful attempts demonstrate better
biomechanical optimization and more efficient use of kinetic energy during the execution
of exercises. The results of this study indicate that an earlier entry into the second phase of
movement, with a higher position of the feet and hips and a smaller shoulder joint angle,
allows for a more efficient initiation of the open end of the kinetic chain. Consequently,
this results in greater peripheral and angular velocities, which are crucial for the successful
execution of gymnastics elements.
The findings of this study complement existing knowledge about kinetic energy in
sports and confirm the importance of energy transfer through the kinetic chain, especially
in gymnastics, where the demand for biomechanical analysis is increasing to enhance
execution techniques. This knowledge will further contribute to improving performance

Life 2025,15, 172 13 of 14
fluidity while minimizing the risk of injury. Beyond gymnastics, these findings are also
confirmed in other sports, highlighting the universality of biomechanical principles that
can be applied across various disciplines to optimize performance.
Author Contributions: Conceptualization, S.V.; methodology, S.V., M.M., E.K. and S.B.; software,
S.V. and M.M.; validation, D.Ð., P.V., E.K., C.-E.S., A.-M.C., N.-L.V., A.-M.V., S.B., D.S., B.B., N.A.
and T.D.; formal analysis, D.Ð., P.V. and M.M.; investigation, S.V., D.Ð., P.V., M.M., E.K., S.B.
and D.S.; resources/data curation, S.V., C.-E.S., A.-M.C., N.-L.V., A.-M.V., B.B., N.A. and T.D.;
writing—original
draft preparation, D.Ð., P.V., C.-E.S., A.-M.C., N.-L.V., A.-M.V., D.S., B.B., N.A.
and T.D.;
writing—review
and editing, S.V., D.Ð., M.M., E.K., S.B. and T.D.; visualization, D.Ð., P.V.,
C.-E.S., A.-M.C., N.-L.V., A.-M.V., D.S., B.B., N.A. and T.D.; supervision, S.V., E.K. and T.D.; project
administration, S.V. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: The study was conducted in accordance with the Declaration
of Helsinki, and approved by the Gymnastics Federation of Serbia on 27 October 2023 (approval No.
11-485/23) for studies on humans.
Informed Consent Statement: Informed consent was obtained from the subject involved in the study.
Data Availability Statement: The data provided in this study can be obtained upon request from the
corresponding author.
Conflicts of Interest: The authors declare no conflicts of interest.
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