## Foundations Of Mechanics |

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### Contents

Calculus on Manifolds | 60 |

ANALYTICAL DYNAMICS | 159 |

HamiltonJacobi Theory and Mathematical Physics | 370 |

Copyright | |

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### Common terms and phrases

action assume basis called canonical chart classical Clearly closed orbit compact complete computation condition connected consider constant continuous converges coordinates corresponding critical point defined Definition denote derivative determined diffeomorphism differential dimension discussion elements energy equations equivalent example Exercise exists fact fiber Figure flow formula function geodesic given gives Hamiltonian Hence identity implies integral curve invariant ISBN isomorphism Lagrangian Lemma linear locally manifold means measure mechanics metric momentum motion natural neighborhood nondegenerate Note obtain operator orientation periodic Poincaré preserving problem Proof Proposition prove regular relation relative respect restricted result Riemannian satisfying Sect smooth stability structure submanifold Suppose surface symplectic symplectic manifold tangent theorem theory topology transformation unique vector bundle vector field vector space volume write zero