Himalaya Senapati

Chennai Mathematical Institute · Physics

This thesis studies instabilities and singularities in a geometrical approach to the planar 3-body problem as well as instabilities, chaos and ergodicity in the 3-rotor problem. Trajectories of the planar 3-body problem are expressed as geodesics of the Jacobi-Maupertuis (JM) metric on the configuration space $C^3$. Translation, rotation and scalin...

In the classical three rotor problem, three equal point masses move on a circle subject to attractive cosine potentials of strength g. In the center of mass frame, energy E is the only known conserved quantity. In earlier works [Krishnaswami and Senapati, Indian Acad. Sci. Conf. Ser. 2(1), 139 (2019), and Chaos 29(12), 123121 (2019)], an order–chao...

This paper concerns the classical dynamics of three coupled rotors: equal masses moving on a circle subject to attractive cosine interparticle potentials. This system arises as the classical limit of a model of coupled Josephson junctions. In appropriate units, the non-negative energy E of the relative motion is the only free parameter. We find fam...

In the classical three rotor problem, three equal point masses move on a circle subject to attractive cosine potentials of strength g. In the center of mass frame, energy E is the only known conserved quantity. In earlier work [arXiv:1811.05807], an order-chaos-order transition was discovered in this system along with a band of global chaos for 5.3...

The classical three-body problem arose in an attempt to understand the effect of the Sun on the Moon's Keplerian orbit around the Earth. It has attracted the attention of some of the best physicists and mathematicians and led to the discovery of chaos. We survey the three-body problem in its historical context and use it to introduce several ideas...

This paper concerns 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. Moreover, the quantized system of n-rotors has been used to model coupled Josephson junctions. Unlike in the gravitational problem, there ar...

We study the equal-mass classical three rotor problem, a variant of the three body problem of celestial mechanics. The quantum N-rotor problem arises via a partial continuum limit of the Wick rotated XY model. In units of the coupling, the energy serves as a control parameter. We find periodic `pendulum' and `breather' orbits at all energies and ch...

The Maupertuis principle allows us to regard classical trajectories as reparametrized geodesics of the Jacobi-Maupertuis (JM) metric on configuration space. We study this geodesic reformulation of the planar three-body problem with both Newtonian and attractive inverse-square potentials. The associated JM metrics possess translation and rotation is...

The Maupertuis principle allows us to regard classical trajectories as reparametrized geodesics of the Jacobi-Maupertuis (JM) metric on configuration space. We study this geodesic reformulation of the planar three-body problem with both Newtonian and inverse-square potentials. The associated JM metrics possess translation and rotation isometries in...