Mechanical Systems, Classical Models: Volume III: Analytical Mechanics (Hardcover)

Table of Contents - continued from Volume 1 and 2: Preface 18. Langrangian Mechanics - 1. Preliminary results; 2. Langrange's equations; 3. Other problems concerning Lagrange's equations. 19. Hamiltonian Mechanics - 1. Hamilton's equations; 2. The Hamilton-Jacobi method. 20. Variational Principles. Canonical Transformations - 1. Variational principles; 2. Canonical transformations; 3. Symmetry transformations. Noether's theorem. Conservation laws. 21. Other Considerations on Analytical Methods in Dynamics of Discrete Mechanical Systems - 1. Integral invariants. Ergodic theorems; 2. Periodic motions. Action - angle variables; 3. Methods of exterior differential calculus. Elements of invariantive mechanics; 4. Formalisms in the dynamics of mechanical systems; 5. Control systems. 22. Dynamics of Non-Holonomic Mechanical Systems - 1. Kinematics of non-holonomic mechanical systems; 2. Lagrange's equations. Other equations of motion; 3. Gibbs - Appell equations; 4. Other problems on the dynamics of non-holonomic mechanical systems. 23. Stability and Vibrations - 1. Stability of mechanical systems; 2. Vibrations of mechanical systems. 24. Dynamical Systems. Catastrophes and Chaos - 1. Continuous and discrete dynamical systems; 2. Elements of the theory of catastrophes; 3. Periodic solutions. Global bifurcations; 4. Fractals. Chaotic motions. References.