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Reduced motion equations of an axisymmetric body spinning on a horizontal surface via Lie symmetries

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Abstract

In this paper, the general analytical solution of the mechanical system consisting of an axisymmetric body spinning on a horizontal surface is analyzed. The motion equations are given by a three-dimensional system in which one of the equations is of second order. The invariance of the system under time translation is applied to reduce the order of the system by means of the classical Lie reduction method. As a result, a reduced autonomous first-order system is obtained. It is also explained how to recover the general analytical solution of the original system from the general solution of the reduced motion equations. Finally, some particular situations are considered with the goal of developing further the expression of the analytical solution found. The case of a spinning polar spheroid is also addressed.

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Acknowledgements

A. Ruiz thanks the financial support from FEDER–Ministerio de Ciencia, Innovación y Universidades–Agencia Estatal de Investigación, via the project PGC2018-101514-B-I00 and from Junta de Andalucía to the research group FQM–377. C.H.C.C. Basquerotto is grateful for the financial support provided by the Brazilian National Council for Scientific and Technological Development (CNPq - Brazil) in grant number 426050/2018-5.

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  1. Departamento de Matemáticas, Universidad de Cádiz - UCA, 11510, Puerto Real, Spain

    Adrián Ruiz

  2. Instituto de Geociências e Engenharias, Faculdade de Engenharia Mecânica, Universidade Federal do Sul e Sudeste do Pará, Marabá, Pará, 68505-080, Brazil

    Cláudio H. C. Costa Basquerotto

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Correspondence to Cláudio H. C. Costa Basquerotto.

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Ruiz, A., Basquerotto, C.H.C.C. Reduced motion equations of an axisymmetric body spinning on a horizontal surface via Lie symmetries. Acta Mech 233, 3853–3865 (2022). https://doi.org/10.1007/s00707-022-03306-3

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