Symplectic structures and Hamiltonians of a mechanical system

G.F. Torres del Castillo, G. Mendoza Torres

Abstract


It is shown that in the case of a mechanical system with a finite number of degrees of freedom in classical mechanics, any constant of motion can be used as Hamiltonian by defining appropriately the symplectic structure of the phase space (or, equivalently, the Poisson bracket) and that for a given constant of motion, there are infinitely many symplectic structures that reproduce the equations of motion of the system.

Keywords


Symplectic structure; Hamilton equations

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Revista Mexicana de Física

ISSN: In Process

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