Shane D Ross

Shane D Ross
Verified
Shane verified their affiliation via an institutional email.
Verified
Shane verified their affiliation via an institutional email.
  • PhD, Caltech
  • Professor at Virginia Tech

Professor at Virginia Tech in Aerospace & Ocean Engineering, working on dynamical systems, fluids, and orbital mechanics

About

185
Publications
92,912
Reads
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6,420
Citations
Introduction
The Ross Dynamics Lab applies nonlinear dynamics, performing mathematical modeling, simulation, visualization, and experiments in several different fields, including: 3-body problem orbital mechanics, dispersal in the atmospheric and ocean, coupled translational-rotational dynamics, aerodynamic gliding (e.g., gliding animal dynamics, autorotating samaras), biomechanics, dynamic buckling of flexible structures, transport across the air-water interface, disease spread, and vehicle dynamics.
Current institution
Virginia Tech
Current position
  • Professor
Additional affiliations
August 2019 - present
Virginia Tech
Position
  • Professor (Full)
September 1999 - June 2004
California Institute of Technology
Position
  • Research Assistant
August 2017 - August 2019
Virginia Tech
Position
  • Managing Director
Education
September 1999 - June 2004
California Institute of Technology
Field of study
  • Control and Dynamical Systems
September 1994 - June 1998

Publications

Publications (185)
Article
Full-text available
Harmful algal blooms (HABs) are a threat to aquatic ecosystems worldwide. New information is needed about the environmental conditions associated with the aerosolization and transport of HAB cells and their associated toxins. This information is critical to help inform our understanding of potential exposures. We used a ground-based sensor package...
Article
Full-text available
Flying snakes (genus Chrysopelea) glide without the use of wings. Instead, they splay their ribs and undulate through the air. A snake's ability to glide depends on how well its morphing wing-body produces lift and drag forces. However, previous kinematics experiments under-resolved the body, making it impossible to estimate the aerodynamic load on...
Article
Full-text available
For the recently legalized US hemp industry (Cannabis sativa), cross-pollination between neighboring fields has become a significant challenge, leading to contaminated seeds, reduced oil yields, and in some cases, mandated crop destruction. As a step towards assessing hemp cross-pollination risk, this study characterizes the seasonal and spatial pa...
Article
Full-text available
Invasive species such as insects, pathogens, and weeds reaching new environments by traveling with the wind, represent unquantified and difficult‐to‐manage biosecurity threats to human, animal, and plant health in managed and natural ecosystems. Despite the importance of these invasion events, their complexity is reflected by the lack of tools to p...
Book
Full-text available
Space missions which reach destinations such as the moon, asteroids, or the satellites of Jupiter are complex and challenging to design, requiring new and unusual kinds of orbits to meet their goals, orbits that cannot be found by classical approaches to the problem. In addition, libration point orbits are seeing greater use. This book guides the...
Conference Paper
Full-text available
Understanding the dynamical structure of cislunar space beyond geosynchronous orbit is of significant importance for lunar exploration, as well as for design of high Earth-orbiting mission trajectories in other contexts. A key aspect of these dynamics is the presence of mean motion resonances, as heteroclinic connections between unstable resonant o...
Conference Paper
Full-text available
Lunar mean-motion resonances (MMRs) significantly shape cislunar dynamics beyond GEO forming stable-unstable pairs, with corresponding intermingled chaotic and regular regions. The resonance zone is rigorously defined using the separatrix of unstable resonant periodic orbits surrounding stable quasi-periodic regions. Our study leverages the restric...
Article
Saharan dust events, having great ecological and environmental impacts, are the largest producers of the world’s dust by far. Identifying the mechanisms by which the dust is transported across the Atlantic is crucial for obtaining a complete understanding of these important events. Of these events, the so-called "Godzilla" dust intrusion of June 20...
Preprint
Full-text available
For the recently legalized US hemp industry (Cannabis sativa), cross-pollination between neighboring fields has become a significant challenge, leading to contaminated seeds, reduced oil yields, and in some cases, mandated crop destruction. As a step towards assessing hemp cross-pollination risk, this study characterizes the seasonal and spatial pa...
Preprint
Full-text available
Saharan dust events, having great ecological and environmental impacts, are the largest producers of the world's dust by far. Identifying the mechanisms by which the dust is transported across the Atlantic is crucial for obtaining a complete understanding of these important events. Of these events, the so-called ``Godzilla'' dust intrusion of June...
Conference Paper
Full-text available
Arboreal animals face challenges in maneuvering through complex terrain, and directed aerial descent or gliding flight offers a solution despite control difficulties. While some animals possess specialized structures for aerodynamic control, many arboreal species may rely on tail-assisted attitude control in mid-air. This study examines the role of...
Chapter
Full-text available
Gliding locomotion has convergently evolved in multiple vertebrate and invertebrate taxa, spanning terrestrial and aquatic animals. The selective pressures attributed to the evolution of gliding include the topography of the environment as well as the capabilities for rapidly escaping predation, foraging over larger spatial areas, and landing safel...
Article
Full-text available
The adverse economic impacts of harmful algal blooms can be mitigated via tailored forecasting methods. Adequate provision of these services requires knowledge of the losses avoided, or, in other words, the economic benefits they generate. The latter can be difficult to measure for broader population segments, especially if forecasting services or...
Article
Full-text available
New wind sensing technologies are needed to measure atmospheric flows in aquatic environments where hazardous agents may be present and conventional atmospheric sensors are difficult to deploy. Here, we present the application of model-based multirotor sUAS (small uncrewed aircraft system) wind estimation to measure atmospheric flow variations in a...
Article
Full-text available
Little is known about the transport and fate of aerosolized particles associated with harmful algal blooms (HABs). An Airborne DROne Particle-monitoring System (AirDROPS) was developed and used to monitor, collect, and characterize airborne particles over two HABs in Grand Lake St Marys (GLSM) and Lake Erie (LE), Ohio USA in August 2019. The AirDRO...
Article
Full-text available
Freshwater harmful algal blooms (HABs), caused mostly by toxic cyanobacteria, produce a range of cyanotoxins that threaten the health of humans and domestic animals. Climate conditions and anthropogenic influences such as agricultural run-off can alter the onset and intensity of HABs. Little is known about the distribution and spread of freshwater...
Article
Full-text available
In the circular restricted three-body problem, low energy transit orbits are revealed by linearizing the governing differential equations about the collinear Lagrange points. This procedure fails when time-periodic perturbations are considered, such as perturbation due to the sun (i.e., the bicircular problem) or orbital eccentricity of the primari...
Preprint
Full-text available
In the circular restricted three-body problem, low energy transit orbits are revealed by linearizing the governing differential equations about the collinear Lagrange points. This procedure fails when time-periodic perturbations are considered, such as perturbation due to the sun (i.e., the bicircular problem) or orbital eccentricity of the primari...
Article
Full-text available
An accurate forecast of the red tide respiratory irritation level would improve the lives of many people living in areas affected by algal blooms. Using a decades-long database of daily beach conditions, two conceptually different models to forecast the respiratory irritation risk level one day ahead of time are trained. One model is wind-based, us...
Article
Full-text available
Decreased movement symmetry is associated with injury risk and accelerated disease progression. Methods to analyze continuous data either cannot be used in pathologic populations with abnormal movement patterns or are not defined in terms easily incorporated into clinical care. The purpose of this study was to develop a method of describing symmetr...
Article
Full-text available
This work serves as a bridge between two approaches to analysis of dynamical systems: the local, geometric analysis, and the global operator theoretic Koopman analysis. We explicitly construct vector fields where the instantaneous Lyapunov exponent field is a Koopman eigenfunction. Restricting ourselves to polynomial vector fields to make this cons...
Preprint
Full-text available
An accurate forecast of the red tide respiratory irritation level would improve the lives of many people living in areas affected by algal blooms. Using a decades-long database of daily beach conditions, two conceptually different models to forecast the respiratory irritation risk level one day ahead of time are trained. One model is wind-based, us...
Preprint
Full-text available
This work serves as a bridge between two approaches to analysis of dynamical systems: the local, geometric analysis and the global, operator theoretic, Koopman analysis. We explicitly construct vector fields where the instantaneous Lyapunov exponent field is a Koopman eigenfunction. Restricting ourselves to polynomial vector fields to make this con...
Article
Full-text available
Ocean hazardous spills and search and rescue incidents are becoming more prevalent as maritime activities increase across all sectors of society. However, emergency response time remains a factor due to the lack of information available to accurately forecast the location of small objects. Existing drifting characterization techniques are limited t...
Article
Full-text available
Escape from a potential well through an index-1 saddle can be widely found in some important physical systems. Knowing the criteria and phase space geometry that govern escape events plays an important role in making use of such phenomenon, particularly when realistic frictional or dissipative forces are present. We aim to extend the study of the e...
Preprint
Full-text available
Escape from a potential well through an index-1 saddle can be widely found in some important physical systems. Knowing the criteria and phase space geometry that govern escape events plays an important role in making use of such phenomenon, particularly when realistic frictional or dissipative forces are present. We aim to extend the study the esca...
Article
Full-text available
Invariant manifolds play an important role in organizing global dynamical behaviors. For example, it is found that in multi-well conservative systems where the potential energy wells are connected by index-1 saddles, the motion between potential wells is governed by the invariant manifolds of a periodic orbit around the saddle. In two-degree-of-fre...
Article
Full-text available
Inspired by the application of differential correction to initial-value problems to find periodic orbits in both the autonomous and non-autonomous dynamical systems, here differential correction is applied to boundary-value problems. As a numerical demonstration, the snap-through buckling of circular arches in structural mechanics are selected as e...
Data
A transition ellipsoid for a two mode model of the snap-through of a shallow arch with dissipation
Article
Full-text available
Maple trees (genus Acer) accomplish the task of distributing objects to a wide area by producing seeds, known as samaras, which are carried by the wind as they autorotate and slowly descend to the ground. With the goal of supporting engineering applications, such as gathering environmental data over a broad area, we developed 3D-printed artificial...
Conference Paper
Full-text available
In the circular restricted three-body problem, low-energy transit orbits are revealed by linearizing the governing differential equations about the Lagrange points. This procedure fails when time-periodic perturbations are considered, such as perturbation due to the sun (i.e., the bicircular problem) or orbital eccentricity of the primaries. For th...
Preprint
Full-text available
Ocean hazardous spills and search and rescue incidents are more prevalent as maritime activities increase across all sectors of society. However, emergency response time remains a factor due to a lack of information to accurately forecast the location of small objects. Existing drifting characterization techniques are limited to objects whose drift...
Article
Full-text available
There are two main strategies for improving the projection-based reduced order model (ROM) accuracy—(i) improving the ROM, that is, adding new terms to the standard ROM; and (ii) improving the ROM basis, that is, constructing ROM bases that yield more accurate ROMs. In this paper, we use the latter. We propose two new Lagrangian inner products that...
Preprint
Full-text available
Maple trees (genus Acer) accomplish the task of distributing objects to a wide area by producing seeds which are carried by the wind as they slowly descend to the ground, known as samaras. With the goal of supporting engineering applications, such as gathering environmental data over a broad area, we developed 3D-printed artificial samaras. Here, w...
Preprint
Full-text available
Invariant manifolds play an important role in organizing global dynamical behaviors. For example, it is found that in multi-well conservative systems where the potential energy wells are connected by index-1 saddles, the motion between potential wells is governed by the invariant manifolds of a periodic orbit around the saddle. In two degree of fre...
Article
Full-text available
When flying snakes glide, they use aerial undulation. To determine if aerial undulation is a flight control strategy or a non-functional behavioural vestige of lateral undulation, we measured snake glides using high-speed motion capture and developed a new dynamical model of gliding. Reconstructions of the snake’s wing-body reveal that aerial undul...
Article
Full-text available
An amendment to this paper has been published and can be accessed via a link at the top of the paper.
Article
Full-text available
Lagrangian techniques, such as the finite-time Lyapunov exponent (FTLE) and hyperbolic Lagrangian coherent structures, have become popular tools for analyzing unsteady fluid flows. These techniques identify regions where particles transported by a flow will converge to and diverge from over a finite-time interval, even in a divergence-free flow. La...
Article
Full-text available
Every year, hundreds of people die at sea because of vessel and airplane accidents. A key challenge in reducing the number of these fatalities is to make Search and Rescue (SAR) algorithms more efficient. Here, we address this challenge by uncovering hidden TRansient Attracting Profiles (TRAPs) in ocean-surface velocity data. Computable from a sing...
Preprint
Full-text available
Lagrangian techniques, such as the finite-time Lyapunov exponent (FTLE) and hyperbolic Lagrangian coherent structures (LCS), have become popular tools for analyzing unsteady fluid flows. These techniques identify regions where particles transported by a flow will converge to and diverge from over a finite-time interval, even in a divergence-free fl...
Article
Full-text available
We present a model-based approach to estimate the vertical profile of horizontal wind velocity components using motion perturbations of a multirotor unmanned aircraft system (UAS) in both hovering and steady ascending flight. The state estimation framework employed for wind estimation was adapted to a set of closed-loop rigid body models identified...
Article
Full-text available
Identifying atmospheric transport pathways is important to understand the effects of pollutants on weather, climate, and human health. The atmospheric wind field is variable in space and time and contains complex patterns due to turbulent mixing. In such a highly unsteady flow field, it can be challenging to predict material transport over a finite...
Preprint
Full-text available
We present a model-based approach to wind velocity profiling using motion perturbations of a multirotor unmanned aircraft system (UAS) in both hovering and steady ascending flight. A state estimation framework was adapted to a set of closed-loop rigid body models identified for an off-the-shelf quadrotor. The quadrotor models used for wind estimati...
Article
Full-text available
Even the most simplified models of falling and gliding bodies exhibit rich nonlinear dynamical behavior. Taking a global view of the dynamics of one such model, we find an attracting invariant manifold that acts as the dominant organizing feature of trajectories in velocity space. This attracting manifold captures the final, slowly changing phase o...
Preprint
Full-text available
Every year hundreds of people die at sea because of vessel and airplane accidents. A key challenge in reducing the number of these fatalities is to make Search and Rescue (SAR) algorithms more efficient. Here we address this challenge by uncovering hidden TRansient Attracting Profiles (TRAPs) in ocean-surface velocity data. Computable from a single...
Article
Full-text available
This paper details a new method to estimate the location of unstable equilibria, specifically saddle-points, based on transient trajectories from experiments. We describe a system in which saddle-points (not easily observed in a direct sense)influence the behavior of trajectories that pass ’close-by’ them. This influence is used to construct a mode...
Preprint
Full-text available
Escape from a potential well can occur in different physical systems, such as capsize of ships, resonance transitions in celestial mechanics, and dynamic snap-through of arches and shells, as well as molecular reconfigurations in chemical reactions. The criteria and routes of escape in one-degree of freedom systems has been well studied theoretical...
Article
Full-text available
Small unmanned aircraft systems (sUAS) are rapidly transforming atmospheric research. With the advancement of the development and application of these systems, improving knowledge of best practices for accurate measurement is critical for achieving scientific goals. We present results from an intercomparison of atmospheric measurement data from the...
Preprint
Full-text available
This paper introduces the trajectory divergence rate, a scalar field which locally gives the instantaneous attraction or repulsion of adjacent trajectories. This scalar field may be used to find highly attracting or repelling invariant manifolds, such as slow manifolds, to rapidly approximating hyperbolic Lagrangian coherent structures, or to provi...
Article
Full-text available
The transport of material through the atmosphere is an issue with wide ranging implications for fields as diverse as agriculture, aviation, and human health. Due to the unsteady nature of the atmosphere, predicting how material will be transported via the Earth’s wind field is challenging. Lagrangian diagnostics, such as Lagrangian coherent structu...
Article
Full-text available
This paper introduces the trajectory divergence rate, a scalar field which locally gives the instantaneous attraction or repulsion of adjacent trajectories. This scalar field may be used to find highly attracting or repelling invariant manifolds, such as slow manifolds, to rapidly approximate hyperbolic Lagrangian coherent structures, or to provide...
Article
Full-text available
Concentrations of airborne chemical and biological agents from a hazardous release are not spread uniformly. Instead, there are regions of higher concentration, in part due to local atmospheric flow conditions which can attract agents. We equipped a ground station and two rotary-wing unmanned aircraft systems (UASs) with ultrasonic anemometers. Fli...
Article
Full-text available
The equilibrium configuration of an engineering structure, able to withstand a certain loading condition, is usually associated with a local minimum of the underlying potential energy. However, in the nonlinear context, there may be other equilibria present, and this brings with it the possibility of a transition to an alternative (remote) minimum....
Article
Full-text available
A phase space boundary between transition and non-transition, similar to those observed in chemical reaction dynamics, is shown experimentally in a macroscopic system. We present a validation of the phase space flux across rank one saddles connecting adjacent potential wells and confirm the underlying phase space conduits that mediate the transitio...
Article
Full-text available
Natural aquatic environments such as oceans, lakes, and rivers are home to a tremendous diversity of microorganisms. Some may cross the air-water interface within droplets and become airborne, with the potential to impact the Earth’s radiation budget, precipitation processes, and spread of disease. Larger droplets are likely to return to the water...
Data
Raw data for droplets and bacteria counts from lab experiments These are data from lab experiments using the flume and highspeed video.
Preprint
Full-text available
This paper proposes a Lagrangian data-driven reduced order model (ROM) for an efficient and relatively accurate numerical simulation of the finite time Lyapunov exponent (FTLE) field. To generate the ba- sis, the new Lagrangian ROM explicitly uses Lagrangian data (i.e., the FTLE field) in addition to the Eulerian data (i.e., the velocity field); th...
Preprint
A phase space boundary between transition and non-transition, similar to those observed in chemical reaction dynamics, is shown experimentally in a macroscopic system. We present a validation of the phase space flux across rank one saddles connecting adjacent potential wells and confirm the underlying phase space conduits that mediate the transitio...
Article
Full-text available
Even the most simplified models of falling and gliding bodies exhibit rich nonlinear dynamical behavior. Taking a global view of the dynamics of one such model, we find an attracting invariant manifold that acts as the dominant organizing feature of trajectories in velocity space. This attracting manifold acts as a higher-dimensional analogue to th...
Preprint
Lobe dynamics and escape from a potential well are general frameworks introduced to study phase space transport in chaotic dynamical systems. While the former approach studies how regions of phase space are transported by reducing the flow to a two-dimensional map, the latter approach studies the phase space structures that lead to critical events...
Article
Full-text available
Flying snakes of genus Chrysopelea possess a highly dynamic gliding behavior, which is dominated by an undulation in the form of lateral waves sent posteriorly down the body. The resulting high-amplitude periodic variations in the distribution of mass and aerodynamic forces have been hypothesized to contribute to the stability of the snake’s glidin...
Article
Full-text available
In this paper, we show a low energy Earth–Moon transfer in the context of the Sun–Earth–Moon–spacecraft 4-body system. We consider the 4-body system as the coupled system of the Sun–Earth–spacecraft 3-body system perturbed by the Moon (which we call the Moon-perturbed system) and the Earth–Moon–spacecraft 3-body system perturbed by the Sun (which w...
Article
Full-text available
Escape from a potential well is a paradigm to understand critical events in chemical physics, celestial mechanics, structural mechanics, and ship dynamics, to name but a few. The consequences of escape could be desirable or undesirable depending on the specific problem at hand, however, the general question is how escape occurs and the effects of e...
Preprint
The equilibrium configuration of an engineering structure, able to withstand a certain loading condition, is usually associated with a local minimum of the underlying potential energy. However, in the nonlinear context, there may be other equilibria present, and this brings with it the possibility of a transition to an alternative (remote) minimum....
Article
Full-text available
Lobe dynamics and escape from a potential well are general frameworks introduced to study phase space transport in chaotic dynamical systems.While the former approach studies how regions of phase space get transported by reducing the flow to a two-dimensional map, the latter approach studies the phase space structures that lead to critical events b...
Article
Full-text available
Gliding flight—moving horizontally downward through the air without power—has evolved in a broad diversity of taxa and serves numerous ecologically relevant functions such as predator escape, expanding foraging locations, and finding mates, and has been suggested as an evolutionary pathway to powered flight. Historically, gliding has been conceptua...
Article
Full-text available
Aerial drones and chaos theory help researchers explore the many ways that microorganisms spread havoc around the world
Conference Paper
Full-text available
Predicting the escape from a potential energy well is a universal exercise, governing myriad engineering and natural systems, e.g., buckling phenomena, ship capsize, and human balance. Criteria and routes of escape have previously been determined for 1 degree of freedom (DOF) mechanical systems with time-varying forcing, with reasonable agreement w...
Article
Full-text available
Fusarium head blight (FHB), caused by the plant pathogen Fusarium graminearum, is a significant threat to small grains production worldwide. Additional knowledge is required to clarify the influence of meteorological conditions on the release of ascospores of F. graminearum. Here, a new application of causality analysis is used to determine how met...
Article
Full-text available
The finite-time Lyapunov exponent (FTLE) is a powerful Lagrangian concept widely used for describing large-scale flow patterns and transport phenomena. However, field experiments usually have modest scales. Therefore, it is necessary to bridge the gap between the concept of FTLE and field experiments. In this paper, two independent observations are...
Article
Full-text available
The health and financial cost of falls has spurred research to differentiate the characteristics of fallers and non-fallers. Postural stability has received much of the attention with recent studies exploring various measures of entropy. This study compared the discriminatory ability of several entropy methods at differentiating two paradigms in th...
Article
Full-text available
Many high-risk plant pathogens are transported over long distances (hundreds of meters to thousands of kilometers) in the atmosphere. The ability to track the movement of these pathogens in the atmosphere is essential for forecasting disease spread and establishing effective quarantine measures. Here, we discuss the scales of atmospheric dispersal...
Article
Full-text available
The time-varying finite time Lyapunov exponent (FTLE) is a powerful Lagrangian concept widely used for describing large-scale flow patterns and transport phenomena. However, field experiments usually have modest scales. Therefore, it is necessary to bridge between the powerful concept of FTLE and (local) field experiments. In this paper a new inter...
Article
Full-text available
To obtain more realistic approximations of atmospheric Lagrangian coherent structures, the material surfaces which form a template for the Lagrangian transport, two concepts are considered. First, the effect of unresolved turbulent motion due to finite spatiotemporal resolution of velocity field data is studied and the resulting qualitative changes...
Article
Full-text available
This work presents two new methods for computing finite-time Lyapunov exponents (FTLEs) from noisy spatiotemporally resolved experimentally measured image data of the type used for particle image velocimetry (PIV) or particle tracking velocimetry (PTV). These new approaches are based on the simple insight that the particle images recorded during PI...
Article
Full-text available
We present an experimental approach for estimating finite-time Lyapunov exponent fields (FTLEs) in three-dimensional multi-component or multi-phase flows. From time-resolved sequences of particle images, we directly compute the flow map and coherent structures, while avoiding and outperforming the computationally costly numerical integration. Perfo...
Article
Full-text available
Flying snakes use their entire body as a continuously morphing ‘wing’ to produce lift and shallow their glide trajectory. Their dominant behavior during gliding is aerial undulation, in which lateral waves are sent posteriorly down the body. This highly dynamic behavior, which is unique among animal gliders, should have substantial effects on the f...
Article
Full-text available
Prussin, A. J., II, Li, Q., Malla, R., Ross, S. D., and Schmale, D. G., III. 2014. Monitoring the long-distance transport of Fusarium graminearum from field-scale sources of inoculum. Plant Dis. 98:504-511. The fungus Fusarium graminearum causes Fusarium head blight (FHB) of wheat. Little is known about dispersal of the fungus from field-scale sour...
Article
Full-text available
The fungus Fusarium graminearum causes Fusarium head blight (FHB) of wheat. Little is known about dispersal of the fungus from field-scale sources of inoculum. We monitored the movement of a clonal isolate of F. graminearum from a 3,716 m(2) (0.372 ha) source of inoculum over two field seasons. Ground-based collection devices were placed at distanc...
Article
Full-text available
Fusarium head blight (FHB) is a devastating disease of wheat and barley caused by the fungus Fusarium graminearum. The fungus produces spores that may be transported over long distances in the atmosphere. In order to predict the atmospheric transport of F. graminearum, the production and release of ascospores must be known. We conducted a series of...
Article
Full-text available
In 1991, the Japanese Hiten mission used a low energy transfer with a ballistic capture at the Moon which required less ΔV than a standard Hohmann transfer to the Moon. In this paper, we apply the same dynamical systems techniques used to produce the “Petit Grand Tour” of Jovian moons to reproduce a Hiten-like mission. We decouple the Sun-Earth-Moo...
Article
This work provides an experimental method for simultaneously measuring finite time Lyapunov exponent fields for multiple particle groups, including non-flow tracers, in three-dimensional multiphase flows. From sequences of particle images, e.g., from experimental fluid imaging techniques, we can directly compute the flow map and coherent structures...
Article
Full-text available
The aerobiology of fungi in the genus Fusarium is poorly understood. Recent work has highlighted the role of Lagrangian coherent structures (LCSs) in the movement of fusaria in the lower atmosphere. Here, we extend this work by examining the relationship between the length of atmospheric sampling intervals with autonomous unmanned aerial vehicles (...

Questions

Questions (2)
Question
I haven't seen this addressed in the references I'm using to teach a class on Hamiltonian mechanics.
Question
Given a linear ODE, x'=Ax, where A is a Hamiltonian matrix, I transform via x=Ty s.t. T^(-1)AT is in Jordan canonical form. Is T a symplectic matrix?
Essentially, I want to know if the transformation to the eigenbasis of a linear Hamiltonian system is a symplectic transformation (also called a canonical transformation). I suspect that in general it will not be, unless one is careful with the scaling of the eigenvectors before placing in the columns of T, but I haven't found any obvious answers to this question in texts on Hamiltonian Dynamics (Meyer & Hall, Marsden & Ratiu, Arnold).
It might be helpful to think about this question another way:
   For a linear Hamiltonian system, it is possible to find a symplectic transformation which puts the system in Jordan canonical form?
In practice, I am considering x in R^n where n is 4 or higher (n even). Let J be the canonical symplectic matrix (sometimes called the Poisson matrix). A Hamiltonian matrix (also called an infinitesimally symplectic matrix) is one such that
               JA + ATJ=0
And T being symplectic means TTJT=J

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