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Two dimensional examples of the Jacobi-Maupertuis metric

Hamiltonian systems, from topology to applications through analysis II November 26, 2018 - November 30, 2018

November 27, 2018 (10:30 AM PST - 11:30 AM PST)
Speaker(s): Richard Moeckel (University of Minnesota Twin Cities)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification
Video

6-Moeckel

Abstract

The orbits of a Hamiltonian system on a fixed energy level can be viewed as geodesics of the corresponding Jacobi-Mauptertuis metric on the configuration space.  For systems of two degrees of freedom, this is a metric on the two-dimensional configuration space.  In this talk I will look at some simple examples from celestial mechanics, starting with the Kepler problem and moving on to the collinear and isosceles three-body problems.  I will look at the problem of visualizing the Kepler surface by embedding it in Euclidean space and discuss questions about length-minimizing geodesics for the three-body problems.

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Video/Audio Files

6-Moeckel

H.264 Video 6-Moeckel.mp4 233 MB video/mp4 Download
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