Abstract
This chapter presents several of the most important concepts from analytical dynamics. We derive Lagrange’s equation and how it can be used for the derivation of governing equations of motion. It is, especially, useful for the derivation of the equations of motion for systems, discrete or continuous, with more than one degree-of-freedom, where the Newtonian free body diagrams become more difficult to apply. We also derive Hamilton’s principleHamilton’s Principle, an integral energy formulation, also applicable to both discrete and continuous systems, and see how it is related to Lagrange’s equation. Hamilton’s Hamilton’s Principle is, especially, relevant to the work in Chaps. 10.1007/978-3-030-26133-7_4 and 10.1007/978-3-030-26133-7_5.