Hamiltonian and Lagrangian Dynamics

Hamiltonian and Lagrangian Dynamics (HLD) are two interrelated regimes and sets of techniques that can be used to solve Classical Mechanics problems, like Newtonian Physics does, but HLD is much more powerful and flexible, making manageable the otherwise intractable. In addition, HLD provides intuitive insight and guides approximation techniques. Most importantly, HLD is a foundation for Quantum Mechanics, Quantum Field Theory, Elementary Particle Physics, and Solid State Physics. This...
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Hamiltonian and Lagrangian Dynamics (HLD) are two interrelated regimes and sets of techniques that can be used to solve Classical Mechanics problems, like Newtonian Physics does, but HLD is much more powerful and flexible, making manageable the otherwise intractable. In addition, HLD provides intuitive insight and guides approximation techniques. Most importantly, HLD is a foundation for Quantum Mechanics, Quantum Field Theory, Elementary Particle Physics, and Solid State Physics. This book emphasizes geometric reasoning in both the text and exercises. Volume 1 is devoted to the necessary mathematics: Linear Algebra, Functional Analysis, Manifolds, and Lie Groups. Volume 2 is devoted to physics: Dynamical Systems, Newtonian Physics, Hamiltonian and Lagrangian Dynamics, and many applications. Volume 1 contains unusually concise, yet deep, treatments of Linear Algebra, Lie Groups and of Conic Sections, so that some may wish to use the book to pursue those goals alone. The book is intended to be useful for physics undergraduates in a first course in Analytical Mechanics, and for Graduate students in physics. Mathematics students will find here simple treatments of advanced mathematical topics, and see their practical application. Engineers will also find succor herein for solving difficult problems.