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Borisov, Alexey / Mamaev, Ivan S.

Rigid Body Dynamics

Together with Higher Education Press Ltd. Comp.

Series:De Gruyter Studies in Mathematical Physics 52

    119,95 € / $137.99 / £109.00*

    eBook (EPUB)
    Publication Date:
    December 2018
    ISBN
    978-3-11-054297-4
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    Overview

    • Systematic presentation of rigid body dynamics, covering both classical and recent results
    • Includes extensive illustrations to facilitate understanding
    • Of interest to applied mathematicians and physicists as well as to engineers.

    Aims and Scope

    This book provides an up-to-date overview of results in rigid body dynamics, including material concerned with the analysis of nonintegrability and chaotic behavior in various related problems. The wealth of topics covered makes it a practical reference for researchers and graduate students in mathematics, physics and mechanics.

    Contents
    Rigid Body Equations of Motion and Their Integration
    The Euler – Poisson Equations and Their Generalizations
    The Kirchhoff Equations and Related Problems of Rigid Body Dynamics
    Linear Integrals and Reduction
    Generalizations of Integrability Cases. Explicit Integration
    Periodic Solutions, Nonintegrability, and Transition to Chaos
    Appendix A : Derivation of the Kirchhoff, Poincaré – Zhukovskii, and Four-Dimensional Top Equations
    Appendix B: The Lie Algebra e(4) and Its Orbits
    Appendix C: Quaternion Equations and L-A Pair for the Generalized Goryachev – Chaplygin Top
    Appendix D: The Hess Case and Quantization of the Rotation Number
    Appendix E: Ferromagnetic Dynamics in a Magnetic Field
    Appendix F: The Landau – Lifshitz Equation, Discrete Systems, and the Neumann Problem
    Appendix G: Dynamics of Tops and Material Points on Spheres and Ellipsoids
    Appendix H: On the Motion of a Heavy Rigid Body in an Ideal Fluid with Circulation
    Appendix I: The Hamiltonian Dynamics of Self-gravitating Fluid and Gas Ellipsoids

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    Alexey V. Borisov and Ivan S. Mamaev, Udmurt State University, Russia.

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