Classical Dynamics: A Contemporary ApproachAdvances in the study of dynamical systems have revolutionized the way that classical mechanics is taught and understood. Classical Dynamics, first published in 1998, is a comprehensive textbook that 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). The book contains many worked examples and over 200 homework exercises. 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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analog andthe angle angular momentum approximation axis becomes calculated called canbe canonical equations Cantor set components conserved constant constraint coordinate system defined depends derivative differential equation dimension discussion disks dynamical system dynamical variable eigenvalues eigenvectors ellipse equations of motion example finite firstorder fixed point force frequency function harmonic oscillator hence image FIGURE implies independent inertial initial conditions integral curves intersection inthe invariant inverted KAM theorem kinetic energy Lagrange’s Lagrangian linear manifold matrix Newton’s nonlinear obtained ofthe onedimensional oneform onefreedom orbit parameter particle pendulum perturbation theory phase portrait plane Poincaré map Poisson bracket positive potential problem region righthand side rotation scattering Section shows soliton solution space stable submanifold surface tangent theorem torus tothe trajectory transformation twodimensional unstable unstable manifold values vector field velocity wave write written yields zero