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https://doi.org/10.1007/s11071-008-9430-7

has been cited by the following article:

• 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.