2.00 pm, Lecture Hall 5
Periodic orbits and stability in the classical three-rotor problem
Himalaya Senapati
Chennai Mathematical Institute.
30-01-19

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Abstract

This talk is based on the classical dynamics of three coupled rotors: equal masses moving on a circle subject to cosine inter-particle potentials. It is a simpler variant of the gravitational three body problem and has also been used to model coupled Josephson junctions. We find analogues of the Euler-Lagrange family of periodic solutions: pendulum and isosceles solutions at all energies E. Interestingly, the pendulum solutions alternate between being stable and unstable, with the transition energies accumulating from either side at E = 4. We also study the stability of trajectories by computing the curvature of the Jacobi-Maupertuis metric on the configuration space. Remarkably, this curvature goes from being strictly positive to having either sign when E exceeds four. These two phenomena appear to coincide with the onset of chaos in this system.