Mathematical Methods of Analytical Mechanics

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.

• Helps readers understand calculations surrounding the geometry of the tensor and the geometry of the calculation of the variation
• Presents principles that correspond to the energy conservation of material systems
• Defines the invariance properties associated with Noether's theorem
• Discusses phase space and Liouville's theorem
• Identifies small movements and different types of stabilities

Applied mathematicians and physicists who wish to obtain a rapid knowledge of the basics of analytical mechanics under a very geometric aspect. Physicists who are involved in statistical mechanics and use classical theorems of the space of phases in mechanics

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