Particle on a Torus Knot: A Hamiltonian Analysis

Article Type

Research Article

Publication Title

Foundations of Physics

Abstract

We have studied the dynamics and symmetries of a particle constrained to move in a torus knot. The Hamiltonian system turns out to be Second Class in Dirac’s formulation and the Dirac brackets yield novel noncommutative structures. The equations of motion are obtained for a path in general where the knot is present in the particle orbit but it is not restricted to a particular torus. We also study the motion when it is restricted to a specific torus. The rotational symmetries are studied as well. We have also considered the behavior of small fluctuations of the particle motion about a fixed torus knot.

First Page

1649

Last Page

1665

DOI

10.1007/s10701-016-0035-6

Publication Date

12-1-2016

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