On Equilibrium Positions in the Problem of the Motion of a System of Two Bodies in a Uniform Gravity Field

Valentin Irtegov,Tatiana Titorenko

doi:10.1007/978-3-031-14788-3_10

On Equilibrium Positions in the Problem of the Motion of a System of Two Bodies in a Uniform Gravity Field

Valentin Irtegov, Tatiana Titorenko

https://doi.org/10.1007/978-3-031-14788-3_10

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Publication Date: Jan 1, 2022

Citations: 1

Affiliation: Institute for System Dynamics and Control Theory

#Uniform Gravity Field #One-dimensional Invariant Manifolds + Show 8 more

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Abstract

AbstractIn the problem of motion of a system of two rigid bodies connected by a spherical hinge in a uniform gravity field, the conditions for the existence of two- and one-dimensional invariant manifolds are presented, and the manifolds themselves are found with the use of computer algebra tools. From a mechanical point of view, these solutions correspond to equilibrium positions of the system. Their instability in the first approximation is proved.

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