Foundations Of MechanicsBasic Books, 21 janv. 1978 - 806 pages Foundations of mechanics: a mathematical exposition of classical mechanics with an introduction to the qualitative theory of dynamical systems and applications to the three-body problem. This text, based on the classic first edition of 1967, has been radically expanded to include, in full detail, all the important developments of the past decade. The introductory mathematics (Part I) has been enlarged to comprise a complete, self-contained text of calculus on manifolds. Formal mechanics (Part II) now contains a new and sophisticated exposition of mechanical systems with symmetry, Lagrangian submanifolds, and new applications, such as quantization. The qualitative theory (Part III) has been completely rewritten to accomodate the new numerous fundamental discoveries from the research frontier, such as bifurcations. The primary applications to the three-body problem (Part IV) has been substantially revised and extended to further illustrate these new results.-- |
Table des matières
Exercises | 17 |
ANALYTICAL DYNAMICS | 159 |
159 | 174 |
Droits d'auteur | |
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Expressions et termes fréquents
action bifurcation bracket called canonical chart closed orbit compact support computation connected constant coordinates cotangent critical point defined Definition denote derivative differential dimension e₁ eigenvalue elliptic energy surface equations equivalent ergodic EX(M example Exercise fiber flow formula function geodesic given Hamiltonian system Hamiltonian vector field Hausdorff Hence identity inner product integral curve invariant ISBN isomorphism Lagrangian Lagrangian submanifold Lemma Lie algebra Lie group linear map Math matrix momentum mapping neighborhood nondegenerate one-form open set orbit cylinder orientation P₁ P₂ Poincaré Proof Proposition prove regular value result Riemannian metric Sect smooth stability submanifold subset subspace Suppose symplectic form symplectic manifold symplectic structure tangent bundle tensor theorem theory topology unique V₁ vector bundle vector space w₁ zero