ABSTRACT
This chapter begins with explanations of the basic principles underpinning Newtonian and analytical mechanics, including generalised coordinates, the principle of virtual work, D'Alembert's principle, Hamilton's principle, Lagrange's equations of motion and influence coefficients. It discusses the vibration of and equations of motion for continuous systems, including beams, plates and cylinders. One way of analysing a mechanical system is to extend Newton's laws for a single particle to systems of particles and use the concepts of force and momentum, both of which are vector quantities. Newton's laws and the conservation laws also apply to bodies and systems of particles as well as to single particles. Hamilton's principle is a consideration of the motion of an entire system between two times, t1 and t2. It is an integral principle and reduces dynamics problems to a scalar definite integral. The chapter summarizes the equations of motion and corresponding solutions for beams, plates and thin cylinders.
