Mathematical Methods of Analytical Mechanics uses tensor geometry and geometry of variation calculation, includes the properties associated with Noether's theorem, and highlights methods of integration, including Jacobi's method, which is deduced. In addition, the book covers the Maupertuis principle that looks at the conservation of energy of material systems and how it leads to quantum mechanics. Finally, the book deduces the various spaces underlying the analytical mechanics which lead to the Poisson algebra and the symplectic geometry.
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Table of Contents
Part 1. Introduction to the variation calculus 1. The elementary methods of variation calculus 2. Variation of a curvilinear integral 3. Noether's Theorem
Part 2. Applications to the analytical mechanics 4. The methods of analytical mechanics 5. Integration method of Jacobi 6. Spaces of mechanics Poisson's brackets
Part 3. Properties of mechanical systems 7. Properties of the phase-space 8. Oscillations and small motions of mechanical systems 9. Stability of periodical systems
