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Rigid body dynamics in non-Euclidean spaces

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Abstract

In this paper, we focus on the study of two-dimensional plate dynamics on the Lobachevskii plane L 2. First of all, we consider the free motion of such a plate, which is a pseudospherical analog of dynamics of the Euler top, and also present an analog of the Euler–Poisson equations enabling us to study the motion of the body in potential force fields having rotational symmetry. We present a series of integrable cases, having analogs in Euclidean space, for different fields. Moreover, in the paper, a partial qualitative analysis of the dynamics of free motion of a plate under arbitrary initial conditions is made and a number of computer illustrations are presented which show a substantial difference of the motion from the case of Euclidean space. The study undertaken in the present paper leads to interesting physical consequences, which enable us to detect the influence of curvature on the body dynamics.

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Authors and Affiliations

  1. Steklov Mathematical Institute of Russian Academy of Sciences, Gubkina st., 8, 119991, Moscow, Russia

    A. V. Borisov & I. S. Mamaev

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  1. A. V. Borisov
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  2. I. S. Mamaev
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Correspondence to A. V. Borisov.

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Borisov, A.V., Mamaev, I.S. Rigid body dynamics in non-Euclidean spaces. Russ. J. Math. Phys. 23, 431–454 (2016). https://doi.org/10.1134/S1061920816040026

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