# Juan Félix San JuanUniversidad de La Rioja (Spain) | UNIRIOJA · Mathematics and Computation

Juan Félix San Juan

Professor

## About

98

Publications

8,926

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

767

Citations

Citations since 2016

## Publications

Publications (98)

A second-order closed-form semi-analytical solution of the main problem of the artificial satellite theory ( $$J_2$$ J 2 contribution) consistent with the Draper Semi-analytic Satellite Theory (DSST) is presented. This paper aims to improve the computational speed of the numerical-based approach, which is only available in the GTDS-DSST version. Th...

The orbital trajectory of artificial satellites around the Earth requires frequent corrections in response to different perturbation forces. The necessary maneuvers can be designed in simulated space environments by propagating Two Line Elements with orbit propagators such as SGP4, which provides the orbital position information at a given epoch. I...

Small corrections in the argument of the latitude can be used to improve the accuracy of the SGP4 orbit propagator. These corrections have been obtained by applying the hybrid methodology for orbit propagation to SGP4, therefore yielding a hybrid version of this propagator. The forecasting part of the hybrid method is based on a state-space formula...

The ever-increasing amount of uncontrolled space objects, known as space debris, poses a risk to space activities due to possible collisions with operational spacecraft. An accurate prediction of their orbit is needed to prevent damages to infrastructure in orbit and on the ground. In the frame of the Spanish Space Surveillance and Tracking (SST) (...

The main goal of this research is to optimize low-thrust collision avoidance maneuvers for both the probability-of-collision between satellites and the propellant expenditure considering a J 2 perturbation model. As a first step, an indirect control method integrated with the current DSST software platform is presented in this paper. We apply numer...

Small corrections in the argument of the latitude can be used to improve the accuracy of the SGP4 orbit propagator. These corrections have been obtained by applying the hybrid methodology for orbit propagation to SGP4, therefore yielding a hybrid version of this propagator. The forecasting part of the hybrid method is based on a state-space formula...

We have developed a semi-analytical theory for low-altitude lunar orbits with the aim of verifying what the minimum order of the gravitational model to be considered should be in order to produce realistic results that can be applied to the analysis and design of real missions. With that purpose, we have considered a perturbation model that compris...

The long-term dynamics of perturbed Keplerian motion is usually analyzed in simplified models as part of the preliminary design of artificial satellites missions. It is commonly approached by averaging procedures that deal with literal expressions in expanded form. However, there are cases in which the correct description of the dynamics may requir...

The long-term dynamics of perturbed Keplerian motion is usually analyzed in simplified models as part of the preliminary design of artificial satellites missions. It is commonly approached by averaging procedures that deal with literal expressions in expanded form. However, there are cases in which the correct description of the dynamics may requir...

The hybrid methodology for orbit propagation is a technique that allows improving the accuracy of any propagator for predicting the future trajectory of a satellite or space-debris object in orbit around the Earth. It is based on modeling the error of the base propagator to be enhanced. Both statistical time-series forecasting methods and machine-l...

In the context of general perturbation theories, the main problem of the artificial satellite analyses the motion of an orbiter around an Earth-like planet, only perturbed by its equatorial bulge or J2 effect. By means of a Lie transform and the Krylov-Bogoliubov-Mitropolsky method, a first-order theory in closed form of the eccentricity is produce...

The solution of multiple-revolution perturbed Lambert problems is a challenging task due to the high sensitivity of the final state to variations of the initial velocity. In this work two different solvers based on high order Taylor expansions and an analytical solution of the J2 problem are presented. In addition, an iteration-less procedure is de...

A parametric study of the orbital lifetimes of objects in super-geostationary, and super-synchronous transfer orbits (Super GTO and SSTO, respectively) has been carried out based on a fast an efficient semi-analytical orbit propagator ad hoc designed. Results are displayed by means of time-reentry maps, each of which requires the propagation of hun...

p>Resumen
Space Situational Awareness current needs demand innovative solutions to the orbit propagation problem, so as to find new algorithms which are simultaneously accurate and fast. The hybrid methodology for orbit propagation constitutes a recent approach based on modeling the error of any orbit propagator with the aim of complementing its c...

Nowadays there is an international consensus that space activities must be managed to minimize debris generation and risk. The paper presents a method for the end-of-life (EoL) disposal of spacecraft in Medium Earth
Orbit (MEO). The problem is formulated as a multiobjective optimization
one, which is solved with an evolutionary algorithm. An impuls...

A hybrid orbit propagator based on the analytical integration of the Kepler problem is designed to determine the future position and velocity of any orbiter, usually an artificial satellite or space debris fragment, in two steps: an initial approximation generated by means of an integration method, followed by a forecast of its error, determined by...

The algorithms used in the construction of a semi-analytical propagator for the long-term propagation of highly elliptical orbits (HEO) are described. The software propagates mean elements and include the main gravitational and non-gravitational effects that may affect common HEO orbits, as, for instance, geostationary transfer orbits or Molniya or...

Two-Line Elements (TLEs) continue to be the sole public source of orbiter observations. The accuracy of TLE propagations through the Simplified General Perturbations-4 (SGP4) software decreases dramatically as the propagation horizon increases, and thus the period of validity of TLEs is very limited. As a result, TLEs are gradually becoming insuffi...

Efficient long-term propagation of orbits is needed for e.g. the design of disposal orbits and analysis of their stability. Semi-analytical methods are suited for this as they combine accuracy and efficiency. However, the semi-analytical modelling of non-conservative forces is challenging and in general numerical quadrature is required to accuratel...

The study presents an analysis of accuracy of observations which are contributing to the maintenance of space object catalogue. After quantifying the uncertainties in optical and radar measurements, the second part of the study presents the error within the mean element orbit determination procedure. A batch least square orbit determination method...

The study presents an analysis of the orbit determination process for maintenance of the space object catalogue. After quantifying the uncertainties in optical and radar measurements, the second part of the study presents the error within the mean element orbit determination procedure. A batch least square orbit determination method which makes use...

The present international concern in space situational awareness has produced a renewed interest in efficient methods for propagation of catalogs of data. Recently, a new technique called high-order transfer map (HOTM) method has been proposed to deal with the problem of perturbed Keplerian dynamics. This technique is based on the numerical integra...

An extension of Deprit’s elimination of the parallax is proposed. This extension takes advantage of the flexibility of the Lie-Deprit method, when the inverse of the Lie operator is applied in order to calculate the generating function of this Lie transform. We have found that, under certain conditions, a function \(\mathcal {F}_{n}\) , belonging t...

In this work we present a new methodology for orbit propagation, the hybrid perturbation theory, based on the combination of an integration method and a prediction technique. The former, which can be a numerical, analytical or semianalytical theory, generates an initial approximation that contains some inaccuracies derived from the fact that, in or...

Deprit’s method has been revisited in order to take advantage of certain arbitrariness arising when the inverse of the Lie operator is applied to obtain the generating function of the Lie transform. This arbitrariness is intrinsic to all perturbation techniques and can be used to demonstrate the equivalence among different perturbation methods, to...

Nowadays there is international consensus that space activities must be managed to minimize debris generation and risk. The paper presents a method for the end-of-life (EoL) disposal of spacecraft in high elliptical orbits (HEO). The time evolution of HEO is strongly affected by Earth’s oblateness and luni-solar perturbation, and this can cause in...

The algebra underlying the elimination of the parallax transformation is known to be useful in relegating short-period effects due to tesseral harmonics of the Geopotential. In the case of low-eccentricity orbits, a judicious selection of the generating function of the relegation algorithm allows for a straightforward simplification. Application to...

A scalable second-order analytical orbit propagator programme based on modern and classical perturbation methods is being developed. As a first step in the validation and verification of part of our orbit propagator programme, we only consider the perturbation produced by zonal harmonic coefficients in the Earth's gravity potential, so that it is p...

Galileo operational orbits are slightly affected by the 3 to 5 tesseral resonance, an effect that can be much more important in the case of disposal orbits. Proceeding by canonical perturbation theory we show that the part of the long-term Hamiltonian corresponding to the non-centralities of the Earth's gravitational potential can be replaced by an...

The elimination of the parallax simplification may deprive the simplified Hamiltonian of the geopotential from some long-period terms of the second order of J2, thus, making the achievement of a mean elements orbit whose long-period effects are the same as in the osculating orbit unsuccessful. We show how the separation of short- and long-period va...

The goal of the Draper Semi-analytical Satellite Theory (DSST) Standalone Orbit Propagator is to provide the same algorithms as in the GTDS orbit determination system implementation of the DSST, without GTDS's overhead. However, this goal has not been achieved. The 1984 DSST Standalone included complete models for the mean element motion but trunca...

Analytical integration in Artificial Satellite Theory may benefit from
different canonical simplification techniques, like the elimination of the
parallax, the relegation of the nodes, or the elimination of the perigee. These
techniques were originally devised in polar-nodal variables, an approach that
requires expressing the geopotential as a Pfaf...

On time scales of interest for mission planning of GNSS satellites, the qualitative motion of the semimajor axis and the node evolves primarily from resonances with the Earth’s gravitational field. The relevant dynamics of GPS orbits, which are in deep 2 to 1 resonance, is modeled with an integrable intermediary that depends only on one angle, the...

Astrodynamics Web Tools, AstrodyToolsWeb (http://tastrody.unirioja.es), is an ongoing collaborative Web Tools computing infrastructure project which has been specially designed to support scientific computation. AstrodyToolsWeb provides project collaborators with all the technical and human facilities in order to wrap, manage, and use specialized n...

Classical procedures for designing Earth’s mapping missions rely on a preliminary frozen-eccentricity orbit analysis. This initial exploration is based on the use of zonal gravitational models, which are frequently reduced to a simple analysis. However, the model may not be accurate enough for some applications. Furthermore, lower order truncations...

Longitude-dependent terms of the geopotential cause nonnegligible short-period effects in orbit propagation of artificial satellites. Hence, accurate analytical and semianalytical theories must cope with tesseral harmonics. Modern algorithms for dealing analytically with them allow for closed form relegation. Nevertheless, current procedures for th...

We present a newapproach in astrodynamics and celestialmechanics fields, called hybrid perturbation theory.Ahybrid perturbation theory combines an integrating technique, general perturbation theory or special perturbation theory or semianalyticalmethod, with a forecasting technique, statistical time series model or computational intelligence method...

We present a new economic hybrid analytical orbit propagator program based on SARIMA models, which approximates to a 4 × 4 tesseral analytical theory for a Quasi-Spot satellite. The J 2 perturbation is described by a first-order closed-form analytical theory, whereas the effects produced by the higher orders of J 2 and the perturbation of the rest...

The long-term effects of a distant third-body on a massless satellite that is orbiting an oblate body are studied for a high order expansion of the third-body disturbing function. This high order may be required, for instance, for Earth artificial satellites in the so-called MEO region. After filtering analytically the short-period angles via avera...

The Hamiltonian formulation of the constant radial propulsive acceleration problem in nondimensional units reveals that the problem does not depend on any physical parameter. The qualitative description of the integrable flow is given in terms of the energy and the angular momentum, showing that the different regimes are the result of a bifurcation...

The long-term effect of lunisolar perturbations on high-altitude orbits is studied after a double averaging procedure that removes both the mean anomaly of the satellite and that of the moon. Lunisolar effects acting on high-altitude orbits are comparable in magnitude to the Earth’s oblateness perturbation. Hence, their accurate modeling does not a...

A higher-order perturbation theory for the rotation of a uniaxial satellite under gravity-gradient torque demonstrates that known special configurations of the attitude dynamics at which the satellite rotates,
on average, as in a torque-free state, are only the result of an early truncation of the secular frequencies
of motion. In addition to provi...

A scalable second-order analytical orbit propagator program (AOPP) is being carried out. This AOPP combines modern and classical perturbation methods in function of orbit types or the requirements needed for a space mission, such as catalog maintenance operations, long period evolution, and so on. As a first step on the validation and verification...

In the context of general perturbation theories, we analyze the motion of an artificial satellite around an Earth-like planet perturbed by the first eight zonal harmonic coefficients. By means of two Lie transforms and the Krylov-Bogoliubov-Mitropolsky method we produce a closed-form second-order analytical theory. Except for the critical inclinati...

In the context of general perturbation theories, we analyze the motion of an artificial satellite around an Earth-like planet perturbed by the first eight zonal harmonic coefficients. By means of two Lie transforms and the Krylov-Bogoliubov-Mitropolsky method we produce a closed-form second-order analytical theory. Except for the critical inclinati...

The increase in the facilities of the general computer algebra system, in particular Mathematica, and hardware evolution have supplied us with the possibility of developing a new environment called MathATESAT. Our new
system collects all the tools necessary to carry out high accuracy analytical theories in order to analyze the quantitative
and qual...

To carry out new families of hybrid analytical orbit propagator programs a new methodology is presented. These families combine
a simplified analytical orbit propagator with statistical time series models. In fact, this approach allows the increase of
accuracy without loss of efficiency in the hybrid propagators as well as integrating the effects o...

In the present paper, using Open Multi-Processing (OpenMP) paradigm, we increase the efficiency of the evaluation program of Poisson series generated by MathATESAT by parallelizing the core of this algorithm. These are the mathematical objects which appear in the process of evaluation of an analytical theory with the purpose of calculating the posi...

An initiative within the realm of Space Surveillance Awareness (SSA) is to create an open source software suite that can provide all space actors access to the basic SSA analysis tools needed to operate safely and efficiently in space. These applications include observation compression, orbit propagators, state transition matrix, weighted least squ...

Nonlinear Dynamics Web Tools is an e‐Science and e‐Learning project which is beginning to be developed in the University of The Rioja. The goal it pursues is to encourage scientific collaboration through Internet at the level of Dynamics Systems, in general, and in Astrodynamics, in particular. In this project a Web‐Site embedding in Moodle is goin...

This paper presents an overview of the initiative based on non-commercial software, which is being carried out in the University of La Rioja, to develop an e-Science and e-Learning Web-Site with the aim to encourage open science and e-Collaboration. This infrastructure is focused on supplying free access to a variety of symbolic and numeric applica...

In this paper, we present a methodology to perform new families of hybrid real-time and analytical orbit propagators which combine a simplified analytical orbit propagator with time series models. When time series analysis is a useful statistical prediction tool, which, from the studies of past observations of this same series, a model can be built...

Analytical theories based on Lie-Deprit transforms are being used so as to simplify the search for families of periodic orbits around planets, natural satellites or asteroids. Normalized equations of motion allow locating the frozen orbit families depending on values of the inclination, eccentricity and semi-major axis. In order to analyze the qual...

In the context of general perturbation theories, we analyze the motion of an artificial satellite around an Earth-like planet perturbed by the first eight zonal harmonic coefficients. By means of two Lie trasforms and the Krylov-Bogoliu-bov-Mitropolsky method we produce a closed-form second-order analytical theory. Except for the critical inclinati...

Analytical theories based on Lie-Deprit transforms are used to ob-tain families of periodic orbits for the problem of an orbiter around the Moon. Low and high orbit models are analyzed. Equilibria of the normalized equations of motion provides the representation of a global portrait of families of frozen orbits depending on values of the inclinatio...

In the analytical approach to the main problem in satellite theory, the consideration of the physical parameters imposes a
lower bound for normalized Hamiltonian. We show that there is no elliptic frozen orbits, at critical inclination, when we
consider small values of H, the third component of the angular momentum. The argument used suggests that...

The dynamics of an orbiter around planetary satellites are modeled using Hill's equations perturbed by the nonsphericity of the satellite. Classically, the long-term behavior of this problem is studied by averaging techniques. The double-averaged problem is integrable. However, tip to second order, it presents a symmetry of direct and retrograde in...

Hill's problem describes the most relevant features in the dynamics around planetary satellites. We consider a system of nondimensional variables, and a small parameter that depends only on the nondimensional semimajor axis. Then, the 3-DOF problem is reduced to1-DOF by means of two Lie transforms. Since a symetry between direct and retrograde incl...

We investigate the secular motion of a spacecraft around the natural satellite of a planet. The satellite rotates synchronously with its mean motion around the planet. Our model takes into account the gravitational potential of the satellite up to the second order, and the third-body perturbation in Hill's approximation. Close to the satellite, the...

The dynamics of an orbiter close to a planetary satellite are known to be unstable from a wide range of inclinations encompassing polar orbits. Taking the Jupiter-Europa system as our model, we use numerically determined periodic orbits to investigate the stability of motion over three-dimensional space for this problem. We have found that the chan...

We investigate the secular motion of a spacecraft around the Jovian moon Europa. Our model takes into account the gravitational potential of Europa up to the second order, and the third body perturbation in Hill's approximation. Close to Europa the ratio of the rotation rate of Europa to the mean motion of the orbiter is small. When considering thi...

The design of spatial missions to Mars requires the development of analytical theories in order to put artificial satellites
in orbit around Mars.
In this paper, we present a complete third order analytical model of a satellite perturbed by the zonal J
2, ..., J
6 harmonics of the Mars potential. Two Lie transformations, the elimination of the Par...

Computer Algebra Systems are developing very fast and it is now possible to use new computational power very efficiently to analytically integrate dynamical systems. However, the task of producing an appropriate program is time consuming and requires a considerable amount of skills and practice. Here the merits of numerical versus computer algebrai...

Kepler’s generalized equation is a transcendental nonlinear equation that must be solved in order to compute the position
and velocity of an artificial satellite at any instant t. In this paper, we propose a method to solve analytically that equation. The method is based on the properties of non canonical
Lie transformations and, under certain cond...

Computer Algebra Systems are developing very fast and it is now possible to use new computational power very efficiently to analytically integrate dynamical systems. However, the task of producing an appropriate program is time consuming and requires a considerable amount of skills and practice. Here the merits of numerical versus computer algebrai...

The importance of the development of analytical theories for the motion of artificial satellites is well known, however the involved algebra makes very difficult each advance in the efficience of such theories. We propose here a method to improve the precision of the theories with less computational effort: a detailed study of the relative value of...

The dynamics of an orbiter close to a planetary satellite is known to be unstable from a wide range of inclinations emcompassing polar orbits. Taking the Jupiter-Europa system as our model, we use numerically determined periodic orbits to investigate the stability of motion over three dimensional space for this problem. We found that the change in...

The first-order analytical theory of spacecraft having significant shape ellipticity about second degree and order gravity field was described. The body was assumed to have uniform rotation around its axis of greatest inertia and this model included all main perturbations such as Keplarian attraction, Coriolis force and ellipticity perturbations. A...

Efficiency in handling Poisson series is essential to obtain high-accuracy analytical theories in celestial mechanics and non-linear dynamics in general. A good knowledge of the mathematical structure of these objects is fundamental to create data structures to store and handle efficiently its equivalent computational object. In this paper we analy...

Special efficient Poisson series processors (PSP) have been created. Poison series appear frequently in problems of non-linear dynamics and celestial mechanics and their size makes their manipulation by means of general computer algebra systems (CAS) inefficient, but the characteristics of the problems suggest the use of general CAS with other gene...

When the elimination of the parallax and the elimination of the perigee is applied to the zonal problem of the artificial satellite, a one-degree of freedom Hamiltonian is obtained. The classical way to integrate this Hamiltonian is by applying the Delaunay normalization, however, changing the time to the perturbed true anomaly and the variable to...

The second part of a research on the Hénon and Heiles system in three dimensions is presented. We focus on motions around the origin, where the system may be treated as a case of three perturbed isotropic harmonic oscillators. It is the only Hamiltonian of the family of axially symmetric cubic potentials in 1–1–1 resonance, which needs at least ord...

The second part of a research on the Hénon and Heiles system in three dimensions is presented. We focus on motions around the origin, where the system may be treated as a case of three perturbed isotropic harmonic oscillators. It is the only Hamiltonian of the family of axially symmetric cubic potentials in 1-1-1 resonance, which needs at least ord...

This paper is the first part of a study of the Hénon and Heiles problem in three dimensions. Due to the axial symmetry of the Hamiltonian, the third component of the angular momentum is an integral and the system is considered as a Hamiltonian with two degrees of freedom. As functions of that integral, we show the existence of three circular trajec...

This paper is the first part of a study of the Hénon and Heiles problem in three dimensions. Due to the axial symmetry of the Hamiltonian, the third component of the angular momentum is an integral and the system is considered as a Hamiltonian with two degrees of freedom. As functions of that integral, we show the existence of three circular trajec...

Analytical theories for the artificial satellite motion involve operations with the so called Poisson series. Even if only a second order theory is required, the amount of terms involved is so huge, that it is almost an impossible task to carry out by hand the theory. Thus, algebraic manipulators are essential in this field, and even more, since ge...

Poisson series appear frequently in problems of non-linear dynamics and celestial mechanics. The size of such mathematical objects makes their manipulation by means of general symbolic processors (GSP) inefficient. Special processors named Poisson series processors (PSP) have been created to handle them in a more efficient way. We propose here a wa...

In the Hénon and Heiles Hamiltonian in three dimensions we study the influence of the integral Λ on its dynamics. We treat the system as a perturbed isotropic oscillator in 1-1-1 resonance. The existence of ellipses as simple periodic orbits is established. We find relative equilibria and bifurcations as functions of Λ.