ABSTRACT
Analytic mechanics is a mathematical science, but it is of high importance for engineers as it provides analytic solutions to fundamental problems of engineering mechanics. At the same time it establishes generally applicable procedures. Mathematical physics texts laid the foundation for these analytic approaches addressing physical problems. This chapter finds analytic solutions for classical mechanical problems of elasticity utilizing Hamilton's principle. The most fitting application is the excitation of an elastic system by displacing it from its equilibrium position. The case of non-conservative systems, where energy loss may occur due to dissipation of the energy, will not be discussed. Hamilton's principle may be extended to non-conservative systems, but the added difficulties do not enhance the discussion of the variational aspects, which is the main focus. The chapter also considers the vibrations of an elastic string.
