The Serret-Andoyer Riemannian metric and Euler-Poinsot rigid body motion | Zendy

Bernard Bonnard | Zendy; Olivier Cots | Zendy; Nataliya Shcherbakova | Zendy

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The Serret-Andoyer Riemannian metric and Euler-Poinsot rigid body motion

Author(s) -

Bernard Bonnard,

Olivier Cots,

Nataliya Shcherbakova

Publication year - 2013

Publication title -

mathematical control and related fields

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.658

H-Index - 21

eISSN - 2156-8472

pISSN - 2156-8499

DOI - 10.3934/mcrf.2013.3.287

Subject(s) - metric (unit) , euler's formula , conjugate points , motion (physics) , invariant (physics) , riemannian geometry , euler angles , mathematics , mathematical analysis , pure mathematics , physics , classical mechanics , mathematical physics , geometry , engineering , operations management

The Euler-Poinsot rigid body motion is a standard mechanical system and is the model for left-invariant Riemannian metrics on SO(3). In this article, using the Serret-Andoyer variables we parameterize the solutions and compute the Jacobi fields in relation with the conjugate locus evaluation. Moreover the metric can be restricted to a 2D surface and the conjugate points of this metric are evaluated using recent work [4] on surfaces of revolution

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