Mark Levi studies dynamical systems through geometry and analysis, with applications to mechanical and physical motion. His research description includes stability, geometric phases, averaging and charged-particle dynamics.
An example of the viewpoint is the inverted pendulum: a rapidly varying drive can stabilize a configuration that is unstable without it. Translating the motion into geometric or averaged descriptions can expose a simpler mechanism than direct inspection of the full trajectory.[ref]
https://www.marklevimath.com/publications. Research areas and mathematical interpretation of physical problems
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