Andoyer's variables and phases in the  free rigid body

Sebastián Ferrer; Francisco J. Molero

doi:10.3934/jgm.2014.6.25

Article Contents

2014, Volume 6, Issue 1: 25-37. Doi: 10.3934/jgm.2014.6.25

This issue Previous Article Aspects of reduction and transformation of Lagrangian systems with symmetry Next Article Fluid-structure interaction in the Lagrange-Poincaré formalism: The Navier-Stokes and inviscid regimes

Andoyer's variables and phases in the free rigid body

Sebastián Ferrer^1, and
Francisco J. Molero^2,

1.
Departamento de Matemática Aplicada, Universidad de Murcia, 30100 Espinardo
2.
Departamento de Matemática Aplicada, Universidad de Murcia, Murcia, 30071 Espinardo

Received: April 30, 2013

Revised: October 31, 2013

Published: February 2014

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Abstract

Using Andoyer's variables we present a new proof of Montgomery's formula by measuring $\Delta\mu$ when $\nu$ has made a rotation. Our treatment is built on the equations of the differential system of the free rigid solid, together with the explicit expression of the spherical area defined by the intersection of the surfaces given by the energy and momentum integrals. We also consider the phase $\Delta\nu$ of the moving frame when $\mu$ has made a rotation around the angular momentum vector, and we give the formula for its computation.

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Mathematics Subject Classification: Primary: 70E15.

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