Two dimensional examples of the Jacobi-Maupertuis metric
Hamiltonian systems, from topology to applications through analysis II November 26, 2018 - November 30, 2018
Location: MSRI: Simons Auditorium
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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