Cases of Complete Integrability in Transcendental Functions in Dynamics and Certain Invariant Indices



The results of this work appeared in the process of studying a certain problem on the rigid body motion in a medium with resistance, where we needed to deal with first integrals having nonstandard properties. Precisely, they are not analytic, not smooth, and on certain sets, they can be even discontinuous. Moreover, they are expressed through a finite combination of elementary functions. However, the latter circumstances allowed us to carry out a complete analysis of all phase trajectories and show those their properties which have a “roughness” and are preserved for systems of a more general form having certain symmetries of latent type. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)