Mathematical Methods of Analytical Mechanics

Mathematical Methods of Analytical Mechanics

1st Edition - November 13, 2020

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  • Author: Henri Gouin
  • Hardcover ISBN: 9781785483158
  • eBook ISBN: 9780128229866

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Description

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.

Key Features

  • 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

Readership

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

Product details

  • No. of pages: 320
  • Language: English
  • Copyright: © ISTE Press - Elsevier 2020
  • Published: November 13, 2020
  • Imprint: ISTE Press - Elsevier
  • Hardcover ISBN: 9781785483158
  • eBook ISBN: 9780128229866

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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