Mathematical Methods of Analytical Mechanics

Erscheinungsjahr 2020
ISBN: 978-1-78548-315-8
Verlag: ISTE PR ELSEVIER

Buch, Englisch, 320 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 599 g

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.

Zielgruppe

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

Autoren/Hrsg.

Gouin, Henri

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Geometrie der modernen Physik
• Naturwissenschaften Physik Mechanik

Inhaltsverzeichnis

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

Über Autor(innen)

Gouin, Henri
Henri Gouin, is a specialist of continuum mechanics in which he has published numerous articles. He holds a BSE, a master's degree, aggregation in mathematics from the University of Paris and Ecole Normale Supérieure de Saint-Cloud, and a PhD and a State Doctorate in mathematics from the University of Provence. Professor at the university, he taught the analytical mechanics course for ten years at the Faculty of Sciences of Marseille. He is now Professor Emeritus at the University of Aix-Marseille, France.