The use of geometric methods in classical mechanics has proven fruitful, with wide applications in physics and engineering. In this book, Professor Marsden concentrates on these geometric aspects, especially on symmetry techniques. The main points he covers are: the stability of relative equilibria, which is analyzed using the block diagonalization technique; geometric phases, studied using the reduction and reconstruction technique; and bifurcation of relative equilibria and chaos in mechanical systems. A unifying theme for these points is provided by reduction theory, the associated mechanical connection and techniques from dynamical systems. These methods can be applied to many control and stabilization situations, and this is illustrated using rigid bodies with internal rotors, and the use of geometric phases in mechanical systems. To illustrate the above ideas and the power of geometric arguments, the author studies a variety of specific systems, including the double spherical pendulum and the classical rotating water molecule.
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"...centres around symmetry and symplectic quotients. Many examples are given illustrating the utility and relevance of symplectic quotients....readable and stimulating." Michael Atiyah, Bulletin of the American Mathematical Society
"...The virtue [of this book] is in the breadth, relevance, and complexity of the examples treated..." Mathematical Reviews
"...The virtue [of this book] is in the breadth, relevance, and complexity of the examples treated..." Mathematical Reviews
Book Description
The use of geometric methods in classical mechanics has proven fruitful, with wide applications in physics and engineering. This text concentrates on these geometric aspects, especially symmetry techniques, and is geared to mathematicians, physicists and engineers.
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First Sentence:
This chapter gives an overview of some of the topics that will be covered so the reader can get a coherent picture of the types of problems and associated mathematical structure that will be developed. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
double spherical pendulum, locked inertia tensor, relative equilibria, energy momentum method, momentum map, coupled rigid bodies, block diagonalization, mechanical integrators, geometric phases, carrier body, symplectic form, relative equilibrium, symplectic structure, homoclinic orbits, discrete symmetry, symplectic manifold, dual pair Key Phrases - Capitalized Phrases (CAPs): (learn more)
Hamiltonian Hopf, G-invariant Hamiltonian, Proof Let, Mechanics Figure New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This chapter gives an overview of some of the topics that will be covered so the reader can get a coherent picture of the types of problems and associated mathematical structure that will be developed. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
double spherical pendulum, locked inertia tensor, relative equilibria, energy momentum method, momentum map, coupled rigid bodies, block diagonalization, mechanical integrators, geometric phases, carrier body, symplectic form, relative equilibrium, symplectic structure, homoclinic orbits, discrete symmetry, symplectic manifold, dual pair Key Phrases - Capitalized Phrases (CAPs): (learn more)
Hamiltonian Hopf, G-invariant Hamiltonian, Proof Let, Mechanics Figure New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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37
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- Numerical Methods (Colloquia Mathematica Societatis Janos Bolyai) by D. Greenspan in Back Matter
- Mode Selective Chemistry (Jerusalem Symposia) by Joshua Jortner in Back Matter
- Symplectic Techniques in Physics by Victor Guillemin in Back Matter
- Elements of the Theory of Representations (Grundlehren der mathematischen Wissenschaften) by A. A. Kirillov in Back Matter
- New Directions in Applied Mathematics: Papers Presented April 25-26, 1980 on the Occasion of the Case Centennial Celebration by P.J. Hilton in Back Matter
See all 20 books this book cites
- Classical Mechanics: Transformations, Flows, Integrable and Chaotic Dynamics by Joseph L. McCauley in Back Matter (1), and Back Matter (2)
- Geometric Mechanics and Symmetry: The Peyresq Lectures (London Mathematical Society Lecture Note Series) by James Montaldi on page 155, and page 400
- Mathematical Control Theory by John B. Baillieul on page 320, and Back Matter
- Symplectic Geometry and Topology (Ias/Park City Mathematics Series, V. 7) by Yakov Eliashberg on page 335, and Back Matter
- Current and Future Directions in Applied Mathematics by Mark Alber on page 63, and Back Matter
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