Linearized Equations

Abstract

In some applications one is interested just in small motions of a multibody system about some known nominal motion. The small motions can be described by the linearized system equations. It is well known, of course, that there are special nonlinear phenomena such as self-excitation, limit cycles, entrainment of frequency and subharmonic oscillations which can appear even for small motions, but cannot be gotten as responses of linear systems. Nevertheless, the linearized equations often are sufficient to represent motion in the vicinity of a nominal motion. The basic equations are first collected here, and variables are then separated into those describing the known nominal motion and others describing the unknown small deviations from it. Ultimately, a linearized state space representation of the motion is developed.