Analytical modeling of the binary dynamic circuit motion

Abstract

The binary dynamic circuit, which can be a design scheme for a number of technical systems is considered in the paper. The dynamic circuit is characterized by the kinetic energy of the translational motion of two masses, the potential energy of these masses’ elastic interaction and the dissipative function of energy dissipation during their motion. The free motion of a binary dynamic circuit is found according to a given initial phase state. A mathematical model of the binary dynamic circuit motion in the canonical form and the corresponding characteristic equation of the fourth degree are compiled. Analytical modeling of the binary dynamic circuit is carried out on the basis of the proposed particular solution of the complete algebraic equation of the fourth degree. A homogeneous dynamic circuit is considered and the reduced coefficients of elasticity and damping are introduced. The dependence of the reduced coefficients of elasticity and damping is established, which provides the required class of solutions to the characteristic equation. An ordered form of the analytical representation of a dynamic process is proposed in symmetric determinants, which is distinguished by the conservatism of notation with respect to the roots of the characteristic equation and phase coordinates.