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

Kuleshov, Alexander S.; Chernyakov, G. A.

doi:10.1007/s10958-020-04705-4

Cited by 1 publication

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“…The papers by Bardin [34, 35] used the Kovacic algorithm to study the orbital stability of periodic motions of a heavy rigid body with a fixed point in the Bobylev–Steklov case. The paper by Kuleshov and Chernyakov [36] used the Kovacic algorithm to study the problem of motion of a heavy rotationally symmetric body on a fixed perfectly rough horizontal plane. The problem of motion of a heavy homogeneous ball, rolling without sliding on the given surface of revolution is studied by Kuleshov and Solomina [37] using the Kovacic algorithm.…”

Section: Introductionmentioning

confidence: 99%

Application of the Kovacic algorithm for the investigation of motion of a heavy rigid body with a fixed point in the Hess case

Bardin¹,

Kuleshov²

2022

Z Angew Math Mech

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In 1890, Hess found new special case of integrability of Euler-Poisson equations of motion of a heavy rigid body with a fixed point. In 1892, Nekrasov proved that the solution of the problem of motion of a heavy rigid body with a fixed point under Hess conditions reduces to integrating the second-order linear differential equation. In this paper, the corresponding linear differential equation is derived and its coefficients are presented in the rational form. Using the Kovacic algorithm, we proved that the Liouvillian solutions of the corresponding secondorder linear differential equation exist only in the case, when the moving rigid body is the Lagrange top, or in the case, when the constant of the area integral is zero.

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Section: Introductionmentioning

confidence: 99%