Hamiltonian and Lagrangian Dynamics

This is a text on Hamiltonian and Lagrangian Mechanics designed for use by students who have just finished the Calculus sequence. However, there is enough advanced material that it could also serve for a first year graduate course in Classical Mechanics. It might be used as a principal text or as a reference, or as a lifeboat, in either case. The book distinguishes itself by providing an unusually geometric approach. Here, we introduce Hamiltonian Dynamics first, as it is more intuitive, since the Hamitonian is the “energy” of the system. Then we develop Lagrangian Dynamics. I have devoted early chapters modern mathematics, meaning Group Theory, Linear Algebra, Functional Analysis, and some Differential Geometry. We then exploit this material to present Dynamical Systems more clearly. This book may also be useful to mathematics students who might want a gentle and painless introduction to modern mathematics, and a chance to see what it can do.