Families of canonical transformations by Hamilton-Jacobi-Poincaré equation. Application to  rotational andorbital motion

Sebastián Ferrer; Martin Lara

doi:10.3934/jgm.2010.2.223

Article Contents

2010, Volume 2, Issue 3: 223-241. Doi: 10.3934/jgm.2010.2.223

This issue Previous Article Next Article Hamiltonian mechanical systems on Lie algebroids, unimodularity and preservation of volumes

Families of canonical transformations by Hamilton-Jacobi-Poincaré equation. Application to rotational and orbital motion

Sebastián Ferrer^1, and
Martin Lara^2,

1.
Departamento de Matemática Aplicada, Universidad de Murcia, 30100 Espinardo
2.
Real Observatorio de la Armada, ES-11 110 San Fernando

Received: September 2009

Revised: August 2010

Published: September 2010

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Abstract

The Hamilton-Jacobi equation in the sense of Poincaré, i.e. formulated in the extended phase space and including regularization, is revisited building canonical transformations with the purpose of Hamiltonian reduction and perturbation theory. We illustrate our approach dealing with attitude and orbital dynamics. Based on the use of Andoyer and Whittaker symplectic charts, for which all but one coordinates are cyclic in the Hamilton-Jacobi equation of the free rigid body motion and Kepler problem, respectively, we provide whole families of canonical transformations, among which one recognizes the familiar ones used in attitude and orbital dynamics. In addition, new canonical transformations are demonstrated.

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Mathematics Subject Classification: Primary: 34C20, 37N05, 47A55; Secondary: 70F15, 70E20, 70H20.

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