Hidden symmetry exposure. The mechanical systems with the hard structure of forces

Abstract:
The problem of the best decoupling of mechanical systems’ motion equations is solved. Structure of symmetry groups corresponding to the found decoupling is considered. Gyroscopic and positional non-conservative forces are taken into account. Presence of the latter goes beyond the scope of compact groups’ theory.
The method for solution of problem of hierarchic  decoupling of the equations’ system is suggested.