The geometric properties of free motion the dynamical systems in the phase space

Formulated the law of the curvature of the phase space with the free movement of dynamical systems. In addition to adopted in classical mechanics classification of motions in the state space as a translational motion of the center of mass and spinor motion around the center of mass in the phase space added classification spinor motion on the surface of a hypersphere and translational motion of the center offset hypersphere. We propose a new paradigm named L. Euler development of mathematical and scientific disciplines, born in the well known “dispute D'Alembert and L.Euler about the string”, namely: “forget about the equation, if the phenomenon is described is found the general solution rather than the equation”.