# Shane D RossVirginia Tech (Virginia Polytechnic Institute and State University) | VT · Department of Aerospace and Ocean Engineering

Shane D Ross

PhD, Caltech

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

## About

170

Publications

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5,689

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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.

Additional affiliations

August 2019 - present

August 2017 - August 2019

August 2006 - August 2017

Education

September 1999 - June 2004

September 1994 - June 1998

## Publications

Publications (170)

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...

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...

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...

Invasive species such as insects, pathogens and weeds reaching new environments by travelling with the wind, represents 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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

A transition ellipsoid for a two mode model of the snap-through of a shallow arch with dissipation

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...

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...

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...

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...

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...

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...

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...

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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....

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...

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...

Raw data for droplets and bacteria counts from lab experiments
These are data from lab experiments using the flume and highspeed video.

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...

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...

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...

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...

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...

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...

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 conce...

Aerial drones and chaos theory help researchers explore the many ways that microorganisms spread havoc around the world

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...

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...

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...