Mathematical Methods of Analytical Mechanics - 1st Edition - ISBN: 9781785483158

Mathematical Methods of Analytical Mechanics

1st Edition

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Authors: Henri Gouin
Hardcover ISBN: 9781785483158
Imprint: ISTE Press - Elsevier
Published Date: 1st April 2020
Page Count: 320
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The book's calculations use tensor geometry and geometry of variation calculation. Invariance properties are associated with Noether's theorem. The methods of integration, as Jacobi's method, are deduced. The Maupertuis principle corresponding to the conservation of energy of material systems leads to quantum mechanics. We deduce the various spaces underlying the analytical mechanics which lead to the Poisson algebra and the symplectic geometry.

Key Features

The aim of this book is to:

  • To study the calculations of the geometry of the tensor and the geometry of the calculation of the variation
  • Understanding the Maupertuis principle that corresponds to the energy conservation of material systems
  • Define the invariance properties associated with the Noether theorem
  • Talking about phase space, Liouville's theorem
  • Identify 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

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


No. of pages:
© ISTE Press - Elsevier 2020
1st April 2020
ISTE Press - Elsevier
Hardcover ISBN:

About the Author

Henri Gouin

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.

Affiliations and Expertise

GOUIN Henri R.Professor, Aix-Marseille University

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