TITLE:
Canonical Treatment of Elliptical Motion
AUTHORS:
Ola A. Jarab’ah
KEYWORDS:
Hamilton Jacobi Equation, Generalized Momentum, Elliptical Motion, Cyclic Coordinate
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.13 No.9,
September
26,
2023
ABSTRACT: The constrained motion of a particle on an elliptical path is studied using Hamiltonian mechanics through Poisson bracket and Lagrangian mechanics through Euler Lagrange equation using non-natural Lagrangian. We calculate the generalized momentumpθand we find that this quantity is not conserved and the conjugate θcoordinate is not a cyclic coordinate.