Classical Dynamics: A Contemporary Approach
Recent advances in the study of dynamical systems have revolutionized the way that classical mechanics is taught and understood. This new and comprehensive textbook provides a complete description of this fundamental branch of physics. The authors cover all the material that one would expect to find in a standard graduate course: Lagrangian and Hamiltonian dynamics, canonical transformations, the Hamilton-Jacobi equation, perturbation methods, and rigid bodies. They also deal with more advanced topics such as the relativistic Kepler problem, Liouville and Darboux theorems, and inverse and chaotic scattering. A key feature of the book is the early introduction of geometric (differential manifold) ideas, as well as detailed treatment of topics in nonlinear dynamics (such as the KAM theorem) and continuum dynamics (including solitons). Over 200 homework exercises are included. It will be an ideal textbook for graduate students of physics, applied mathematics, theoretical chemistry, and engineering, as well as a useful reference for researchers in these fields. A solutions manual is available exclusively for instructors.
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AA variables analog angle angular momentum axis becomes calculated called Cantor set center of mass Chapter completely integrable components conserved constant constraint coordinate system defined depends derivative differential equations dimension discussed disks dynamical system dynamical variable eigenvalues elliptic equations of motion Euler Euler angles example FIGURE finite fixed point force frequency function given harmonic oscillator hence HJ equation implies independent inertial initial conditions integral curves intersect invariant inverted irrational KAM theorem kinetic energy Lagrangian linear matrix moves Noether's theorem nonlinear obtained one-dimensional one-form one-freedom orbit parameter particle pendulum periodic perturbation theory phase portrait physical plane Poisson bracket position potential problem region result right-hand side rotation satisfy scattering Section soliton solution solve stable submanifold surface symmetric tangent theorem tori torus trajectory transformation unstable unstable manifold values vector field wave write written yields zero