KOVALEVSKAYA METHOD IN RIGID-BODY DYNAMICS

An example from the field of rigid body dynamics, possessing a natural physical justification, is presented. The behaviour of the solutions of the equations of motion in the real domain, whatever the initial da ta, is regular; nevertheless, depending on the values of a certain con trol parameter, the solution of the system may branch in the complex t ime plane, and the system will have multi-valued first integrals. A de numerable sequence of single-valued polynomial integrals of arbitraril y high even degree is found (unlike Kovalevskaya's case, in which the degree of the first integral of the Euler-Poisson equations is four). As an extension, a system from non-holonomic mechanics is considered. (C) 1997 Elsevier Science Ltd. All rights reserved.