Part I: Newtonian Mechanics1: Introduction2: Newton's Three Laws3: Energy and Work4: Introductory Rotational Dynamics5: The Harmonic Oscillator6: Wave Mechanics & Elements of Mathematical PhysicsPart II: Langrangian Mechanics7: Introduction8: Coordinates & Constraints9: The Stationary Action Principle10: Constrained Langrangian Mechanics11: Point Transformations in Langrangian Mechanics12: The Jacobi Energy Function13: Symmetries & Langrangian-Hamiltonian-Jacobi Theory14: Near-Equilibrium Oscillations15: Virtual Work & d'Alembert's PrinciplePart III: Canonical Mechanics16: Introduction17: The Hamiltonian & Phase Space18: Hamiltonian's equations & Routhian Reduction19: Poisson Brackets & Angular momentum20: Canonical & Gauge Transformations21: Hamilton-Jacobi Theory22: Liouville's Theorem & Classical Statistical Mechanics23: Constrained Hamiltonian Dynamics24: Autonomous Geometrical Mehcanics25: The Structure of Phase Space26: Near-Integrable SystemsPart IV: Classical Field Theory27: Introduction28: Langrangian Field Theory29: Hamiltonian Field Theory30: Clssical Electromagnetism31: Neother's Theorem for Fields32: Classical Path-IntegralsPart V: Preliminary Mathematics33: The (Not so?) Basics34: Matrices35: Partial Differentiation36: Legendre Transformations37: Vector Calculus38: Differential equations39: Calculus of VariationsPart VI: Advanced Mathematics40: Linear Algebra41: Differential GeometryPart VII: Exam Style QuestionsAppendix A: Noether's Theorem ExploredAppendix B: The Action Principle ExploredAppendix C: Useful RelationsAppendxi D: Poisson & Nambu Brackets ExploredAppendix: Canonical Transformations ExploredAppendix F: Action-Angle Variables ExploredAppendix G: Statistical Mechanics ExploredAppendix H: Biographies

"An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics, with a relaxed and self-contained setting. Lagrangian and Hamiltonian dynamics is the continuation of Newton's classical physics into new formalisms, each highlighting novel aspects of mechanics that gradually build in complexity to form the basis for almost all of theoretical physics. Lagrangian and Hamiltonian dynamics also acts as a gateway to more abstract concepts routed in differential geometry and field theories and can be used to introduce these subject areas to newcomers. Journeying in a self-contained manner from the very basics, through the fundamentals and onwards to the cutting edge of the subject, along the way the reader is supported by all the necessary background mathematics, fully worked examples, thoughtful and vibrant illustrations as well as an informal narrative and numerous fresh, modern and inter-disciplinary applications. The book contains some unusual topics for a classical mechanics textbook. Most notable examples include the 'classical wavefunction', Koopman-von Neumann theory, classical density functional theories, the 'vakonomic' variational principle for non-holonomic constraints, the Gibbs-Appell equations, classical path integrals, Nambu brackets and the full framing of mechanics in the language of differential geometry."--