The Lagrangian equations of motion often take the form of second-order nonlinear differential equations. Such equations rarely admit analytical solutions. In some cases it is possible to linearize the equations of motion by imposition of some acceptable approximations. The linearized equations may then be solved analytically. An important class of such problems is the case of small amplitude oscillations about a position of equilibrium or about a predetermined steady motion. The process of linearization may be carried out on the differential equations or one may introduce the pertinent approximations when the energy and virtual work terms are written down. In this chapter we outline the latter procedure and describe methods of solution for the linearized equations.
KeywordsVirtual Work Steady Motion Small Amplitude Oscillation Virtual Velocity Undamped System
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