Lagrange and Appell-Gibbs approaches in problems of non-holonomic dynamic systems

The kind support of the Czech Science Foundation project No. 17-26353J and of the RVO68378297 institutional support is gratefully acknowledged.Hamiltonian functional and relevant Lagrange equation system are popular tools in investigation of dynamic systems. Various generalizations enable to extend the class of problems concerned slightly beyond conventional limits of a Hamiltonian system. This strategy is very effective particularly concerning 2D and simpler 3D systems. However, the governing differential systems of most non-holonomic 3D systems suffer from inadequate complexity, when deduced using this way. Any analytical investigation of such a governing system is rather impossible and its physical interpretation can be multivalent. For easier analysis particularly of systems with nonholonomic constraints the Appell-Gibbs approach seems to be more effective providing more transparent governing systems