Linearized Dynamic Analysis

Several ways of formulating the differential equations of motion of a multibody system have been presented in Chapter 5. These equations are fully nonlinear in either the independent or dependent coordinates. The solution of these non linear equations is required in order to simulate the dynamic behavior of multibody systems that undergo large displacements and rotations. However, many systems work mostly on the proximity of a fixed or constant dynamic equilibrium configuration. It is very convenient to linearize the equations of motion about this equilibrium configuration, so as to take advantage of the linear analysis tools: fast computation of linear response, eigenvalue analysis, control design by pole placement, or other linear techniques, that are not available or at least are more complicated for the fully nonlinear models.