SYMMETRIES OF THE PHASE PLANE
2016jbw | V.V. Smolyaninov // IMASH RAS, Moscow, Russia; ITEB RAS, Puschino, Russia
Phase portraits are widely used in the theory of oscillations of mechanical and other
systems  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. Kleinís program  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.