On tensor invariants for integrable cases of Euler, Lagrange and Kovalevskaya rigid body motion

A.V. Tsiganov

On tensor invariants for integrable cases of Euler, Lagrange and Kovalevskaya rigid body motion

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arxiv 2410.10109 v1 pith:WE7GTGSN submitted 2024-10-14 nlin.SI math-phmath.DSmath.MP

A.V. Tsiganov This is my paper · ORCID

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keywords invariantstensorbodycaseseulerkovalevskayalagrangemotion

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We discuss global tensor invariants of a rigid body motion in the cases of Euler, Lagrange and Kovalevskaya. These invariants are obtained by substituting tensor fields with cubic on variable components into the invariance equation and solving the resulting algebraic equations using computer algebra systems. According to the Poincar\'{e}-Cartan theory of invariants, the existence of invariant geometric structures raises the question of using them to study the dynamics.

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