BEHAVIOUR, EXAMINATION AND STABILITY OF THE CONSTRAINED MECHANICAL SYSTEM DESCRIBED WITH NONLINEAR EQUATIONS

Abstract

The paper considers motion and stability of a holonomic mechanical system in the vertical plane of an arbitrary force field. Differential equations of motion are created for a given system on the basis of general theorems of dynamics. Insights into generalized coordinates, Lagrange’s equations of the second kind, covariant and Hamilton’s equations are presented. Additionally to numerical procedures in the paper, a review of the theoretical foundations is performed. Also, the conditions of static equilibrium are solved numerically and by applying the intersection of the two curves. The paper introduced kinetic as well as the potential energy of the system. The spatial arrangement of equilibrium positions and behavior of the potential energy in the environment of the equilibrium positions is shown. Finally, the stability of motion for analysis is approached through Lagrange - Dirichlet theorem. Moreover, special attention is paid to examining effects responses of the disturbed and undisturbed system. Nonlinear and linearized equations are obtained in order to check the stability of the system for disturbed and undisturbed motion using Hurwitz stability criterion. Various procedures are verificated by drawing the same conclusions.