Investigation of the Motion of a Heavy Body of Revolution on a Perfectly Rough Plane by the Kovacic Algorithm

A. S. Kuleshov ; G. A. Chernyakov

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 145 (2018), pp. 3-85.

Résumé

Investigation of various problems of mechanics and mathematical physics is reduced to the solution of second-order linear differential equations with variable coefficients. In 1986, American mathematician J. Kovacic proposed an algorithm for solution of a second-order linear differential equation in the case where the solution can be expressed in terms of so-called Liouville functions. If a linear second-order differential equation has no Liouville solutions, the Kovacic algorithm also allows to ascertain this fact. In this paper, we discuss the application of the Kovacic algorithm to the problem of the motion of a heavy body of revolution on a perfectly rough horizontal plane. The existence of Liouville solutions of the problem is examined for the cases where the rolling body is an infinitely thin disk, a disk of finite thickness, a dynamically symmetric torus, a paraboloid of revolution, and a spindle-shaped body.

Détail

Keywords: nonholonomic system, dynamically symmetric body, Kovacic algorithm
Mots-clés : Liouville solutions.

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