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euler−poinsot rigid body motion

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Riemannian metrics on 2D-manifolds related to the Euler−Poinsot rigid body motion ∗
Bernard Bonnard, Olivier Cots, Jean-Baptiste Pomet, Nataliya Shcherbakova
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 20 / Issue 3 / July 2014

Published online by Cambridge University Press:

10 June 2014, pp. 864-893

Print publication:

July 2014
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The Euler−Poinsot rigid bodymotion is a standard mechanical system and it is a model for left-invariant Riemannianmetrics on SO(3). In this article using theSerret−Andoyer variables weparameterize the solutions and compute the Jacobi fields in relation with the conjugatelocus evaluation. Moreover, the metric can be restricted to a 2D-surface, and theconjugate points of this metric are evaluated using recent works on surfaces ofrevolution. Another related 2D-metric on S2 associated to the dynamics of spin particles withIsing coupling is analysed using both geometric techniques and numerical simulations.