Nonintegrability and Integrability in Problems of Mechanics

摘要

The nonintegrability of the three-body problem is due to the absence of an integral different from the energy integral [1-4]. The same situation is found in the problem of motion of a heavy rigid body about a fixed point [5-9], In this case, an additional (fourth) integral has been derived only in the classical cases of Euler-Poinsot, Lagrange, and Kovalevskaya.