SYMMETRIES OF THE PHASE PLANE
2016jbw | V.V. Smolyaninov  // IMASH RAS, Moscow, Russia; ITEB RAS, Puschino, Russia smolian@mail.ru

Phase portraits are widely used in the theory of oscillations of mechanical and other systems [1] as they give complete and evident geometrical representation of all variety of movements of dynamic system under various entry conditions. In the present work new geometrical interpretation of phase portraits of the linear dynamic systems is offered. According to well-known F. Klein’s program [2] any geometry follows represents as the theory of geometrical invariants. Constructive working out of this program is reduced to identification of systems of basic invariants, which generating the metric property for spatial movements. Earlier we used such approach for the purpose of identification kinematic invariants of common chronogeometries, and also the special relativity [3-5]. Here we will consider simple dynamic models of classical mechanics.