Shane Ross, professor of dynamical systems at Virginia Tech in the Kevin T. Crofteon Department of Aerospace and Ocean Engineering. His research has been supported by the NSF and NASA, and he has received awards from NASA and the Americal Institute of Aeronautics and Astronautics for his work on astrodynamics.

Dr. Shane D. Ross

PhD Caltech 2004, Advisor: Marsden
My scientific genealogy visualized
Shane Ross
  • Professor
  • Virginia Tech
  • Aerospace & Ocean Engineering

  • Ross Dynamics Lab description | Contact info

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    Students | Books | Bio | Talks | Videos | Google scholar

    atmospheric transport | astrodynamics | aerobiology
    Highway to the heavens. Math leads spacecraft on joy rides through the solar system.
    Energy efficient paths through space. New Space Force-funded project on Cislunar Space. Introductory video.

    Dynamical systems theory,
    computations, visualization,
    control, and applications

    Funded Projects:
    NASA trans-oceanic dust
    NSF Flying snake fluid mechanics
    NSF Data Science Corps
    USDA Pollen transport
    NSF Lagrangian transport structure
    NSF Dynamic buckling prediction
    NSF Environmental flow hazards
    NSF CAREER Phase space transport
    NSF CMMI Aerobiological mixing
    NSF EFRI Insect fluid control
    NSF BIO Barriers and invasions

    Applications to:
    Dynamics buckling
    Hamiltonian systems
    Structural mechanics
    Experimental mechanics
    Data visualization
    Animal biomechanics
    Plant biomechanics
    Atmospheric transport
    Airborne microbe spread
    Pollution dispersion
    Environmental flow analysis
    Topology of transport
    Stirring & mixing
    Forecasts and predictability
    Lagrangian coherent structutres
    Almost-invariant sets
    Almost-cyclic sets
    Population dynamics
    Optimal control
    Efficient navigation
    Chemical physics
    Chaotic advection
    Dynamical astronomy

  • Publications
  • Slides
  • YouTube
  • Monographs
  • Movies
  • Resume
  • Vita

  • MISC
  • Students
  • Space tubes
  • SBES

  • Co-founder of BIOTRANS (BIOlogical TRANSport interdisciplinary graduate education program, NSF IGERT / IGEP)

    Associate editor for Celestial Mechanics and Dynamical Astronomy

    Jun 2024 Access our group's new article for free, Atmospheric transport structures shaping the "Godzilla" dust plume in Atmospheric Environment, with lead author and PhD candidate Albert Jarvis. See one of the key videos showing an attracting coherent structure bounding a large trans-oceanic airborne dust plume from the Sahara desert. SIAM News wrote an article about this when it was first presented last year.

    Mar 2024 Netflix's hit sci-fi series '3 Body Problem''is based on a real math problem that is so complex it's impossible to solve, interview for Business Insider. Related X thread

    Sep 2023 New Space Force-funded project on Cislunar Space. Watch an introductory video on the orbital dynamics of a spacecraft in the Earth-Moon system.

    Mar 2023 New book chapter, Convergence in Gliding Animals: Morphology, Behavior, and Mechanics in Convergent Evolution, Fascinating Life Sciences. Flying squirrels, lizards, and squid, oh my!

    Feb 2023 LCS Air Bridges across oceans, delivering smoke, and invasive species. New OPEN ACCESS paper, In the wind: Invasive species travel along predictable atmospheric pathways.

    Jan 2023 Sensing atmospheric flows in aquatic environments using multirotor small uncrewed aircraft system (sUAS), new open-access paper in Environmental Science: Atmospheres

    Sep 2022 New paper, Drone-based particle monitoring above two harmful algal blooms (HABs) in the USA in Environmental Science: Atmospheres, Advance Article. *OPEN ACCESS*. DOI 10.1039/d2ea00055e

    Aug 2022 New open access paper: Drone-based water sampling and characterization of three freshwater harmful algal blooms in the United States in Frontiers in Remote Sensing. Video of field campaign.

    Jul 2022 New video lecture series on the 3-Body Problem. See also the accompanying book.

    Jun 2022 Beach-level 24-hour forecasts of Florida red tide-induced respiratory irritation, new paper in Harmful Algae. Related podcast at Data Skeptic

    Apr 2022 Geometry of transit orbits in the periodically-perturbed restricted three-body problem, new paper in Advances in Space Research. Preprint available for free on arXiv. Watch PhD student Josh Fitzgerald's video describing his result.

    Mar 2022 Undergraduates! Apply now for the Data Sciences Summer REU program at Virginia Tech. Deadline is Friday, March 25.

    Dec 2021 Continuous similarity analysis in patient populations, new paper in Journal of Biomechanics.

    Sep 2021 Is the Finite-Time Lyapunov Exponent Field a Koopman Eigenfunction?, new paper in Mathematics

    Aug 2021 Transition criteria and phase space structures in a three degree of freedom system with dissipation, new paper in Journal of Physics A: Mathematical and Theoretical

    Jul 2021 New online course Space Vehicle Dynamics, spacecraft and satellite attitude dynamics, attitude determination and stabilization

    Jun 2021 New course videos introducing Hamiltonian systems

    May 2021 Free university-level course videos on Nonlinear Dynamics and Chaos in short videos focused on specific topics, for those new to the subject, and with several examples.

    May 2021 New paper on Global invariant manifolds delineating transition and escape dynamics in dissipative systems: an application to snap-through buckling, published in Nonlinear Dynamics

    Apr 2021 New freely available paper on Differential correction and arc-length continuation applied to boundary value problems: examples based on snap-through of circular arches, just published in Applied Mathematical Modelling.

    Apr 2021 Open access article on Wind dispersal of natural and biomimetic maple samaras, just published in Biomimetics.

    Mar 2021 New freely available paper on Multirotor-assisted measurements of wind-induced drift of irregularly shaped objects in aquatic environments, just published in Applied Ocean Research. See a short video abstract.

    Jan 2021 Online course videos for Nonlinear Dynamics and Chaos, for those new to the subject.

    Nov 2020 Open access paper on Reduced order modeling of fluids using Lagrangian coherent structures

    Oct 2020 Course videos on Analytical dynamics - Lagrangian and 3D rigid body dynamics. This course on YouTube will ensure that you have a firm grasp of the fundamentals of engineering dynamics, specifically the analytical dynamics approach (Lagrangian mechanics) and 3D rigid body motion. The course will extend your knowledge of dynamics into areas not covered or covered only briefly at the undergraduate level, e.g., Lagrange’s equations, D’Alembert’s principle, quasi-velocities, phase plane analysis. See the class notes in PDF form.

    Jul 2020 Paper on the instantaneous limit of finite-time Lyapunov exponents, calculating repelling and attracting Lagrangian coherent structures from a single velocity snapshot. Paper here.

    Jul 2020 New paper: Undulation enables gliding in flying snakes in Nature Physics. Watch the 9-minute video giving the main findings.

    Jun 2020 Summer short course videos on 'Center manifolds, normal forms, and bifurcations'. Read more about it here on YouTube. See the class notes in OneNote form, or in PDF form here.

    May 2020 Find out how hidden flow structures in the ocean can aid ocean search-and-rescue operations in a new Nature Communications paper (open access). See the press release and ocean experiment video. Authors: M. Serra, P. Sathe, I. Rypina, A. Kirincich, S.D. Ross, P. Lermusiaux, A. Allen, T. Peacock, G. Haller.

    Apr 2020 New video lecture series for my Advanced Dynamics course, posted on YouTube. Topics covered include Hamiltonian systems (canonical and non-canonical), nonlinear dynamics, Poisson brackets, integrals of motion, periodic orbits, quasi-periodic orbits, resonance, nonlinear oscillators, stability, chaos, invariant maniifolds. See the class notes in OneNote or PDF form here.

    Mar 2020 All drones can be used as wind sensors, for providing wind profiles on demand, anywhere, with higher spatiotemporal resolution and a fraction of the cost of other methods. See the free open-access paper in Sensors led by soon-to-graduate aerospace PhD student Javier Gonzalez-Rocha.

    Feb 2020 Identifying air pollution transport patterns using generalized Lagrangian coherent structure. See the free open-access paper in Atmosphere.

    Jan 2020 We're starting a new Harnessing the Data Revolution: Data Science Corps program for college students this year, where those in training to be engineers/physicists and biologists team up to tackle problems in data-driven decision-making at the engineering/biology interface. The main part of this multi-university program is a summer experience at Virginia Tech, for student-directed field research and data analysis. Read the news article.

    Jan 2020 All drones are wind sensors. Detecting wind from the motion of multirotor drones. See the paper here on 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.

    Nov 2019 Calculating Lagrangian coherent structures (LCS) from the instantaneous limit of the finite-time Lyapunov exponent (FTLE), with several examples to geophysical flows. See the paper here on the instantaneous Lyapunov exponent (iLE) and related iLE structures.

    Oct 2019 Find out how hidden flow structures in the ocean can aid Coast Guard search-and-rescue operations. See the paper here.

    Oct 2019 Researchers receive USDA grant to study transport of pollen from genetically engineered switchgrass and hemp. See the news article about a new project by David Schmale, Hosein Foroutan, and me.

    Jul 2019 In N degrees of freedom, the boundary of orbits escaping across an index-1 saddle, starting at the same initial energy, goes from a (2N-2)-dimensional hyper-cylinder in the conservative case to a (2N-2)-dimensional hyper-ellipsoid in the dissipative case. See the paper here.

    Jul 2019 News piece on a special edition of Scientific American on "Wild Ideas in Science" that features an article by me and David Schmale on the transport of microbes in the air and water. There's an 'atmospheric superhighway' that transports microbes across the globe, modeled using fluid dynamics and mathematics, and sampled using drones. The special issue covers what it calls "amazing innovations that just might save the planet and us".

    Jun 2019 We present a new data-driven method to estimate the location and type of unstable equilibrium points from observed dynamics in mechanical systems of two or more degrees of freedom. Such unstable points are not easily found directly, based on transient trajectories from experiments, but can have a large influence on global dynamics. Our method is validated experimentally for a simple bench-top system, showing promise for more complicated systems. See the paper.

    May 2019 Get our new open access paper, a massive experimental comparison paper led by Lindsay Barbieri of the University of Vermont, on intercomparison of small unmanned aircraft system (sUAS) measurements for atmospheric science during the large LAPSE-RATE campaign. Special thanks to David Schmale and Javier Gonzalez-Rocha for piloting the multirotor drones for VT-UVA and contributing our data.

    May 2019 Download our new paper for free on global phase space structures in a model of passive descent, with simplied models of behaviors such as tumbling leaves, gliding animals, etc. More here, including interactive visualization of the 3D phase space structures.

    Apr 2019 Field campaign exposes students to data and decisions research at the interface of engineering and biology. See the news article about the Spring Break REU campaign put on by David Schmale and me.

    Apr 2019 See our new Nonlinear Dynamics paper on a trajectory-free approximation of phase space structures using the trajectory divergence rate. More here.

    Mar 2019 Congratulations to Peter Nolan on passing his PhD defense! See his defense talk on Youtube here and read his thesis on Experimental and Theoretical Developments in the Application of Lagrangian Coherent Structures to Geophysical Transport

    Mar 2019 See our new open access free Sensors paper on a method for detecting atmospheric Lagrangian coherent structures using a single fixed wing unmanned aircraft system. More here.

    Feb 2019 See the 1-minute NSF video about our group's work on predicting the motion of material at the ocean surface, with applications to search-and-rescue, oil spills, and harmful algal blooms.

    Dec 2018 New paper on detecting Lagrangian coherent structures directly using simultaneous atmospheric measurments with drones (unmanned aerial vehicles, UAVs) published in Sensors

    Nov 2018 See the press release about a new NSF funded project to apply new applied math techniques to improve forecasts of contaminant spread in the oceans, floods, and atmosphere - combining reduced order modeling and Lagrangian coherent structures. In collaboration with Traian Iliescu in the Virginia Tech Math Dept.

    Nov 2018 New article in Physical Review E on Experimental validation of phase space conduits of transition between potential wells just published. Can also access the 2-pager extended abstract for NODYCON 2019 here.

    Sep 2018 New article on Wind-driven spume droplet production and the transport of Pseudomonas syringae from aquatic environments published open-access in PeerJ. See related video.

    Sep 2018 I will be attending 2018 SACNAS: The National Diversity in STEM Conference in San Antonio, Texas during October 11-13. I will be at the Virginia Tech College of Engineering booth (#520). Email me if you'd like to meet.

    Sep 2018 Interested in graduate school in mechanics? Take integrated coursework on fluids, solids, dynamics, and biomechanics and get a MS or PhD in Engineering Mechanics from Virginia Tech. Apply to visit us for free during our Prospective Student Weekend Oct 19-20. Deadline to apply is September 21. Apply now by filling out a short survey and uploading your CV.

    Aug 2018 See the new video on our recent ocean experiments using simulataneous drone and water-based assets, which has applications to search-and-rescue, hazard containment, oil spills and distaster relief. All part of the NSF Advanced Lagrangian Prediction for Hazards Assessment (ALPHA) project.

    Jul 2018 Congratulations to Gary Nave on defending his thesis to become a PhD! Watch his defense on video here.

    Feb 2018 Congratulations to Isaac Yeaton on defending his thesis to become a PhD!

    Jan 2018 Global dynamics of non-equilibrium gliding in animals has been selected as one of the top 10 Highlights of 2017 by the journal Bioinspiration & Biomimetics, which includes the best and most influential research published in the area

    Dec 2017 Article on A tube dynamics perspective on stability transitions: An example based on snap-through buckling, which extends recent theory to structural mechanics and the effects of dissipation. In collaboration with J. Zhong and L.N. Virgin.

    Oct 2017 Article on Control of gliding in flying snakes, which sets the stage for development of multi-link flying snake robots. In collaboration with F. Jafari, S. Tahmasian, and J.J. Socha.

    Aug 2017 New article on Tube dynamics and low energy Earth-Moon transfers in the 4-body system, on using Lagrangian coherent structures in the time-varying N-body problem to generalize the geometric framework of separatrix tubes in phase space governing escape and capture. In collaboration with Kaori Onozaki and Prof. Hiroaki Yoshimura of Waseda Uniersity (Japan).

    May 2017 New article on a Computational Method for Phase Space Transport with Applications to Lobe Dynamics and Rate of Escape in collaboration with Francois Lekien and former student Shibabrat Naik.

    April 2017 Congratulations to PhD student Gary Nave on receiving the Outstanding Graduate Student Leader award by the Virginia Tech Division of Student Affairs.

    March 2017 New Featured Article in Bioinspiration & Biomimetics on Global dynamics of non-equilibrium gliding in animals with student Isaac Yeaton and Jake Socha. Download for free to learn about dynamical systems analysis of the velocity phase space of animal glides. More info, including supplemental information here.

    February 2017 Congratulations to undergrad researcher Tom Magelinski, chosen as this year's BEAM Outstanding Senior!

    January 2017 Read the article High-Flying Microbes in Scientific American; other info here

    January 2017 Want to know more about high-flying microbes riding air currents across the globe? Check out a video and a scientific review article in addition the Scientific American article

    January 2017 We are still accepting applicants to both the Engineering Science and Mechanics and Biological Transport graduate programs. Contact me for more info.

    January 2017 Ross co-wrote "High-flying microbes", an article on dispersal of airbone microbes via highways in the sky with David Schmale for Scientific American, February 2017 issue. See Virginia Tech press release

    November 2016 Paper on 'Geometry of escaping dynamics in nonlinear ship motion' with S. Naik, applies tube dynamics to the ocean engineering application of ship capsize

    September 2016 Congratulations to Dr. Shibabrat Naik on defending his dissertation to earn a PhD in Engineering Mechanics!

    August 2016 Paper on 'Tube dynamics and low energy trajectory from the earth to the moon in the coupled three-body system' presented at International Conference on Astrodynamics Tools and Techniques

    May 2016 Ross gave a talk on 'Lagrangian transport and mixing in fluids from geometric, probabilistic, and topological perspectives.' at workshop Numerical Analysis and Predictability of Fluid Motion (hosted by the Pitt Math Dept.). See the slides

    March 2016 Congratulations to Dr. Renee Pietsch on defending her dissertation to earn a PhD in Biology!

    Jan 2016 Ross gave a talk on 'Escape from potential wells in multi-dimensional systems: experiments and partial control' at Dynamics Days US 2016 in Durham, NC (hosted by Duke Physics Dept.). See the slides

    Jan 2016 If you're at the 2016 SICB annual meeting in Portland, check out Isaac Yeaton's talk on the highest resolution flying snake experiments ever performed; on Wednesday, Jan 6. (SICB = Society of Integrative and Comparative Biology)

    Dec 2015 Detecting causality: new paper in European Journal of Plant Pathology entitled Identification of meteorological predictors of Fusarium graminearum ascospore release using correlation and causality analyses where we use new methods to detect which environmental factors cause the release of airborne plant pathogens from diseased agricultural fields

    Nov 2015 New paper published in Nonlinear Processes in Geophysics entitled Local finite-time Lyapunov exponent, local sampling and probabilistic source and destination regions where we show the connection between large-scale Lagrangian coherent structures in geophysical flows and consecutively released or collected samples in field experiments. With Amir BozorgMagham and David Schmale. Links to videos here

    Nov 2015 Ross named Virginia Tech Scholar of the Week "for his work to make an unpredictable world more predictable".

    Oct 2015 New paper published in Annals of Biomedical Engineering entitled Comparing Postural Stability Entropy Analyses to Differentiate Fallers and Non-fallers where we show we can predict which elderly adults are prone to falls.

    Sep 2015 Press release on our new NSF project by a multi-university team on forecasting where damaging contaminants in the ocean or atmosphere go.

    Aug 2015 The lab is now on Twitter. Follow us @RossDynamicsLab

    July 2015 Ross and a team of other collaborators at Virginia Tech, MIT, Woods Hole, and Berkeley have been awarded a nearly $3 million grant from the NSF for a project on Advanced Lagrangian Methods for Prediction, Mitigation and Response to Environmental Flow Hazards

    June 2015 New paper published in Annual Review of Phytopathology entitled Highways in the Sky: Scales of Atmospheric Transport of Plant Pathogens. This is a joint review article with my long-time collaborator David Schmale.

    May 2015 Ross gave a talk on 'Experimental Verification of Criteria for Escape from a Potential Well in a Multi-degree of Freedom System' at the SIAM Conference on Applications of Dynamical Systems, Snowbird, Utah.

    Apr 2015 From the archives: Ross' talk on the Interplanetary Superhighway from 2004 is finally on YouTube. So are many other talks and simulations

    Jan 2015 See new paper in the journal Agricultural and Forest Meteorology on Experimental validation of a long-distance transport model for plant pathogens: application to Fusarium graminearum with A.J. Prussin, Sloan Fellow at Virginia Tech/Pittsburgh. Youtube video of pathogen spread here

    Nov 2014 See the dynamics videos which the Dynamics II class (junior-level dynamics, ESM 3124) put together

    Nov 2014 See new paper on Atmospheric Lagrangian coherent structures considering unresolved turbulence and forecast uncertainty with Amir BozorgMagham of the Univ. of Maryland.

    Oct 2014 Ross will be speaking on October 18 at a panel open to the public on 'Contagions' related to the spread of disease. Details here. This is part of the installation ceremonies of Virginia Tech's new university president Timothy Sands. The slides are here (w/o movies).

    Sep 2014 See new paper on Experimental determination of three-dimensional finite-time Lyapunov exponents in multi-component flows in the journal Experiments in Fluids with Georgia Tech postdoc (and former PhD student) Sam Raben

    Aug 2014 Ross speaking at CDS@20, the 20th anniversary of the Control and Dynamical Systems (CDS) PhD program at Caltech. My talk.

    Jun 2014 See new paper on Seasonal associations and atmospheric transport distances of fungi in the genus Fusarium collected with unmanned aerial vehicles and ground-based sampling devices in the journal Atmospheric Environment

    May 2014 See new paper on A theoretical analysis of pitch stability during gliding in flying snakes in the journal Bioinspiration & Biomimetics

    Apr 2014 Ross to give talk at Cornell on May 2, Center for Applied Mathematics colloquium

    Mar 2014 Two new papers on aerobiology appearing in Plant Disease based on MultiSTEPS trainee AJ Prussin's field work, Estimating the Production and Release of Ascospores from a Field-Scale Source of Fusarium graminearum Inoculum and Monitoring the Long-Distance Transport of Fusarium graminearum from Field-Scale Sources of Inoculum

    Feb 2014 Congratulations to Amir BozorgMagham on defending his PhD in Engineering Mechanics!

    Jan 2014 Congratulations to Nick Sharp. His programming team has advanced to the 2014 ACM-ICPC World Finals in Ekaterinurg, Russia this summer.

    Dec 2013 See new paper on Computation of finite time Lyapunov exponents from time resolved particle image velocimetry data in Experiments in Fluids, about improving the accuracy of Lagrangian coherent structure (LCS) calculations from particle tracking in fluid experiments

    Oct 2013 Browse last year's projects in Frontiers in Dynamical Systems. Be sure to request the course for Spring 2014 (see ad)

    Oct 2013 Please sign up for two classes in Spring 2014 which I'm teaching: ESM 6984 SS: Frontiers in Dynamical Systems and ESM 6314 Advanced Dynamics -- links go to the course announcements

    Oct 2013 Two new talks posted: "Geophysical transport structure and ecology: challenges and opportunities" and "Identifying transport structure: set-oriented FTLE, bifurcations of transfer operator modes, and predicting critical transitions"

    Sep 2013 Congratulations to David Schmale for being named one of Popular Science's Brilliant Ten for 2013!

    Aug 2013 From September to December, Ross will be visiting faculty at ICMAT (Institute of Mathematical Sciences) in Madrid, Spain. If you'll be in the area, let me know!

    Aug 2013 Congratulations to Sam Raben on finishing his PhD in Mechanical Engineering and starting as a Joesph Ford Postdoctoral Fellow at Georgia Tech!

    Jul 2013 Ross to speak at workshop in September on Uncovering Transport Barriers in Geophysical Flows at the Banff International Research Station for Mathematical Innovation and Discovery

    May 2013 See new paper on Real-time prediction of atmospheric Lagrangian coherent structures based on forecast data: An application and error analysis in Physica D, with lead author Amir BozorgMagham

    May 2013 Come to my session at Snowbird and hear my talk, (abstract here). Slides of the talk are posted here.

    May 2013 Congratulations to Binbin Lin and A.J. Prussin, who just passed their Ph.D. defenses! Congratulations also to Shibabrat Naik for passing his preliminary exam!

    May 2013 Congratulations to my former student Dr. Phanindra Tallapragada (EM PhD '10), who will join Clemson University as an assistant professor of mechanical engineering in Fall 2013!

    Apr 2013 We found a new faculty member! Congratulations to James Hanna, currently of U Mass, who will be joining ESM in August 2013.

    Dec 2012 New paper on Topological chaos, braiding and bifurcation of almost-cyclic sets published in Chaos (content includes movies under multimedia)

    Oct 2012 My former ESM masters student Jeff Twigg is featured in a press release of the Army Research Lab, Army researchers link ground robots for collaborative autonomy

    Oct 2012 New paper on Capturing near-Earth asteroids around Earth has appeared in Acta Astronautica

    Sep 2012 New paper on A set oriented definition of the finite-time Lyapunov exponents and coherent sets accepted to Communications in Nonlinear Science and Numerical Simulation

    July 2012 Ross receives 2011-12 Liviu Librescu Prize

    July 2012 Tentative schedule of speakers at International Conference on Flow Dynamics (ICFD), September 19-21, 2012 in Sendai, Japan is available here.

    past news


    Why do flying snakes undulate in the air?

    Findings suggest the design of flying snake robots

    Ocean experiments 2018 with simultaneous drone and water-based assets

    Applications to search-and-rescue, hazard release, oil spills

    High-flying Microbes

    Riding highways in the sky

    The Interplanetary Superhighway

    Low energy space transportation

    Flying snake simulation: longitudinal dynamics

    Flying snake trajectory and attitude dynamics, with forces

    Topological chaos, braiding and bifurcation of almost-cyclic sets

    Movie shows switching order of eigenmode branches as a parameter is changed, as well as changes along branches.

    Airborne pathogen spread

    Near-Earth asteroid capture

    nearly 100,000 views this millennium

    Locations of visitors to this page

    interplanetary superhighway, transport network, gravitational corridors