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Canonical Treatment of Elliptical Motion
Applied Physics Department, Faculty of Science, Tafila Technical University, At-Tafilah, Jordan
- 1 Applied Physics Department, Faculty of Science, Tafila Technical University, At-Tafilah, Jordan
Advances in Pure Mathematics·Volume 13 (2023)·Pages 620–624·Published 31 August 2023·DOI10.4236/apm.2023.139041
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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 momentum p θ and we find that this quantity is not conserved and the conjugate θ coordinate is not a cyclic coordinate.
KeywordsHamilton Jacobi EquationGeneralized MomentumElliptical MotionCyclic Coordinate
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