Introduction to Mathematical Methods of Analytical Mechanics presents an overview of geometric methods of calculus and their applications to analytical mechanics. The properties of material systems are studied with a finite number of degrees of freedom, using tensorial geometry and the calculation of variations.
Research into tools, invariance groups and integration methods is essential in order to understand fundamental themes such as wave mechanics, symplectic geometry and celestial mechanics. The book examines Noether's theorem, Jacobi's method, Maupertuis's principle, Poisson's brackets, Liouville's theorem, etc. The study of small movements, including periodic systems and different types of stability, are also major subjects in various fields of science.
Suitable for students in the latter years of a mathematics and physics degree, this book accelerates the development of knowledge of the fundamental methods of mathematical physics. The book concludes with a set of problems with solutions to consolidate the knowledge.
Part 1.Introduction to the Calculus of Variations
1. Elementary Methods to the Calculus of Variations.
2. Variation of Curvilinear Integral.
3. The Noether Theorem.
Part 2. Applications to Analytical Mechanics
4. The Methods of Analytical Mechanics.
5. Jacobi’s Integration Method.
6. Spaces of Mechanics – Poisson Brackets.
Part 3. Properties of Mechanical Systems
7. Properties of Phase Space.
8. Oscillations and Small Motions of Mechanical Systems.
9. The Stability of Periodic Systems.
Part 4. Problems and Exercises
10. Problems and Exercises.
11. Solutions to Problems and Exercises.
Henri Gouin is Professor at Aix-Marseille University, France.
Table of Contents
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