11 AM, Lecture Hall 1
Classical three body problem
Chennai Mathematical Institute.
We begin with a historical review of the classical three body problem. Then we discuss a geometrical approach based on a reformulation of classical trajectories as reparametrized geodesics of the Jacobi-Maupertuis metric on configuration space. Geodesic flow on the full configuration space leads to corresponding flows on its Riemannian quotients by isometries. Extending work of R Montgomery, we obtain results on sectional curvatures which indicate widespread geodesic instabilities in the planar 3 body problem. The geometry near binary and triple collisions is examined and its implications for regularization of collisions and geodesic completeness are discussed. This work is joint with Himalaya Senapati.