Analytical Mechanics

Abstract

This chapter and the next one illustrate the basic principles of Analytical Mechanics. Their purpose is to introduce a number of concepts that are not only useful per se, but also constitute a basis for the concepts of Quantum Mechanics that are introduced in later chapters. The Lagrangian function and the Lagrange equations are derived as a consequence of the variational calculus, followed by the derivation of the Hamiltonian function and Hamilton equations. Next, the Hamilton–Jacobi equation is derived after discussing the time–energy conjugacy. The chapter continues with the definition of the Poisson brackets and the derivation of some properties of theirs, and concludes with the description of the phase space and state space.