This book 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.
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OUVRAGE
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Introduction to Mathematical Methods of Analytical Mechanics
Henri Gouin, IUSTI
first book of a trilogy
