An introduction to Lagrangian and Hamiltonian mechanics

These notes are dedicated to Dr. Frank Berkshire whose enthusiasm and knowledge inspired me as a student. The lecture notes herein, are largely based on the first half of Frank's Dynamics course that I attended as a third year undergraduate at Imperial College in the Autumn term of 1989. Preface Newtonian mechanics took the Apollo astronauts to the moon. It also took the voyager spacecraft to the far reaches of the solar system. However Newto-nian mechanics is a consequence of a more general scheme. One that brought us quantum mechanics, and thus the digital age. Indeed it has pointed us beyond that as well. The scheme is Lagrangian and Hamiltonian mechanics. Its original prescription rested on two principles. First that we should try to express the state of the mechanical system using the minimum representation possible and which reflects the fact that the physics of the problem is coordinate-invariant. Second, a mechanical system tries to optimize its action from one split second to the next. These notes are intended as an elementary introduction into these ideas and the basic prescription of Lagrangian and Hamiltonian mechanics. A prerequisite is the thorough understanding of the calculus of variations, which is where we begin.