Geodesic motion on the symplectic leaf of $SO(3)$ with distorted $e(3)$ algebra and integrability according to Liouville

Дериглазов, А. А.

doi:10.48550/arxiv.2302.04828

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2023

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“…This paper is the fifth in the series [1][2][3][4], devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. In the previous works has been considered the dynamics of a free asymmetric body.…”

Section: Introductionmentioning

confidence: 99%

Has the Problem of the Motion of a Heavy Symmetric Top Been Solved in Quadratures?

Дериглазов¹

2023

Preprint

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We have revised the problem of the motion of a heavy symmetric top. When formulating equations of motion of the Lagrange top with the diagonal inertia tensor, the potential energy has more complicated form as compared with that assumed in the literature on dynamics of a rigid body. Using the Liouville's theorem, we solve the improved equations in quadratures and present the explicit expressions for the resulting elliptic integrals.

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Section: Introductionmentioning

confidence: 99%

Has the Problem of the Motion of a Heavy Symmetric Top Been Solved in Quadratures?

Дериглазов¹

2023

Preprint

View full text Add to dashboard Cite

show abstract

Geodesic motion on the symplectic leaf of $SO(3)$ with distorted $e(3)$ algebra and integrability according to Liouville

Cited by 1 publication

References 7 publications

Has the Problem of the Motion of a Heavy Symmetric Top Been Solved in Quadratures?

Has the Problem of the Motion of a Heavy Symmetric Top Been Solved in Quadratures?

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