Hamilton's Principle and Hamilton's Law of Varying Action

The principle of virtual work was derived after first establishing the relations stemming from the balance of linear momentum. Therein, directly starting from this principle we then described the development of the governing equations for N-body dynamical systems suitable for the subsequent time discretization which is presented in the later chapters of this textbook. In this chapter, in contrast, we provide an alternative formulation and formalism directly starting from Hamilton's principle, and alternatively, also via Hamilton's law of varying action (due to certain concerns as related to logic inconsistencies that exist for transient situations with Hamiltons principle as highlighted subsequently). Nonetheless, the present developments also lead to the same and/or equivalent representations as in the previous chapter, but are formulated from different perspectives.