E-Book Content
Mechanics and Symmetry Reduction Theory Jerrold E. Marsden and Tudor S. Ratiu February 3, 1998
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Preface Preface goes here. Pasadena, CA Spring, 1998
Jerry Marsden and Tudor Ratiu
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Preface
Contents Preface
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1 Introduction and Overview 1.1 Lagrangian and Hamiltonian Mechanics. 1.2 The Euler–Poincar´e Equations. . . . . . 1.3 The Lie–Poisson Equations. . . . . . . . 1.4 The Heavy Top. . . . . . . . . . . . . . . 1.5 Incompressible Fluids. . . . . . . . . . . 1.6 The Basic Euler–Poincar´e Equations. . . 1.7 Lie–Poisson Reduction. . . . . . . . . . . 1.8 Symplectic and Poisson Reduction. . . .
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1 1 3 8 10 11 13 14 20
2 Symplectic Reduction 2.1 Presymplectic Reduction . . . . . . . . . . . . . 2.2 Symplectic Reduction by a Group Action . . . 2.3 Coadjoint Orbits as Symplectic Reduced Spaces 2.4 Reducing Hamiltonian Systems . . . . . . . . . 2.5 Orbit Reduction . . . . . . . . . . . . . . . . . 2.6 Foliation Orbit Reduction . . . . . . . . . . . . 2.7 The Shifting Theorem . . . . . . . . . . . . . . 2.8 Dynamics via Orbit Reduction . . . . . . . . . 2.9 Reduction by Stages . . . . . . . . . . . . . . .
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