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

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 t...

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Bibliographic Details
Published in:Acta mechanica 2022-09, Vol.233 (9), p.3853-3865
Main Authors: Ruiz, Adrián, Basquerotto, Cláudio H. C. Costa
Format: Article
Language:English
Subjects:
Axisymmetric bodies
Classical and Continuum Physics
Control
Dynamical Systems
Engineering
Engineering Fluid Dynamics
Engineering Thermodynamics
Equations of motion
Exact solutions
Heat and Mass Transfer
Mathematical analysis
Mechanical systems
Original Paper
Solid Mechanics
Symmetry
Theoretical and Applied Mechanics
Velocity
Vibration
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Summary: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.
ISSN:0001-5970
1619-6937
DOI:10.1007/s00707-022-03306-3