Abstract
The problem of motion in the free molecular flow of particles of a rigid body with a fixed point, bounded by the surface of an ellipsoid of revolution is considered. This problem is similar in many aspects to the classical problem of motion of a heavy rigid body about a fixed point. In particular, this problem possesses the integrable cases, correspond to the classical Euler – Poinsot, Lagrange and Hess cases of integrability of equations of motion of a heavy rigid body with a fixed point. Equations of motion of the body in the flow of particles are presented in hamiltonian form. Using the theorem on the Liouville – type nonintegrability of Hamiltonian systems near elliptic equilibrium positions we present the necessary conditions for the existence in the considered problem of an additional analytic first integral independent of the energy integral. We proved that the obtained necessary conditions are not fulfilled for the rigid body with a mass distribution corresponding to the classical Kovalevskaya integrable case in the problem of motion of a heavy rigid body with a fixed point.
This research was supported financially by the RFBR (grant no. 20-01-00637).
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Kuleshov, A.S., Gadzhiev, M.M. (2022). Nonintegrability of the Problem of Motion of an Ellipsoidal Body with a Fixed Point in a Flow of Particles. In: Balandin, D., Barkalov, K., Meyerov, I. (eds) Mathematical Modeling and Supercomputer Technologies. MMST 2022. Communications in Computer and Information Science, vol 1750. Springer, Cham. https://doi.org/10.1007/978-3-031-24145-1_5
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