Models of real system nonlinear dynamics abstractions

Abstract

A number of models of the real mechanical system nonlinear dynamics approximations are presented. These models, at the same time, present corresponding models of heavy mass particles
nonlinear dynamics along rotating circle about a fixed vertical as well as skew positioned axis, with constant angular velocity. In the case of circle rotation around vertical axis with constant angular velocity, it is shown that constant weight force of heavy mass particle, in the ideal constraint, and also kinematic constraint, with constant angular velocity of circle rotation about vertical axis, along which heavy mass particle moves, are sources and causes of nonlinear terms in differential equations of it’s dynamics. In the case of circle rotation about skew positioned axis with constant angular velocity, itis shown that constant weight force of heavy mass particle, in the ideal constraint, and also kinematic
constraint, with constant angular velocity of circle rotation about skew positioned axis, along which heavy mass particle moves, are sources and causes not only of appearance of nonlinear terms in differential equations of it’s dynamics, but also of terms depending explicitly on time. Linearizations and linear and nonlinear approximations of corresponding differential equations about stationary points (stationary regimes) are obtained. Analysis of stability and nostability of system nonlinear dynamics
around stationary points (stationary regimes) as well as around relative equilibrium positions of heavy mass particle at circle is presented. It is pointed out that in the phase portraits, a trigger of coupled singularities appears which is a source and cause of possible appearance of chaotic like regimes excited by pure periodical external excitations applied to the mass particle. Also, reasons for investigating the character of local properties of linear as well as nonlinear dynamics around singular points are presented.