TITLE:
Any Hamiltonian System Is Locally Equivalent to a Free Particle
AUTHORS:
Elizabeth Galindo-Linares, Esperanza Navarro-Morale, Gilberto Silva-Ortigoza, Román Suárez-Xique, Magdalena Marciano-Melchor, Ramón Silva-Ortigoza, Edwin Román-Hernández
KEYWORDS:
Hamiltonian System; Canonical Transformation
JOURNAL NAME:
World Journal of Mechanics,
Vol.2 No.5,
October
31,
2012
ABSTRACT: In this work we use the Hamilton-Jacobi theory to show that locally all the Hamiltonian systems with n degrees of freedom are equivalent. That is, there is a canonical transformation connecting two arbitrary Hamiltonian systems with the same number of degrees of freedom. This result in particular implies that locally all the Hamiltonian systems are equivalent to that of a free particle. We illustrate our result with two particular examples; first we show that the one-dimensional free particle is locally equivalent to the one-dimensional harmonic oscillator and second that the two-dimensional free particle is locally equivalent to the two-dimensional Kepler problem.