Foundations of MechanicsAmerican Mathematical Soc., 2008 - 826 pages A reference on symplectic geometry, analytical mechanics and symplectic methods in mathematical physics. It offers a treatment of geometric mechanics. It is also suitable as a textbook for the foundations of differentiable and Hamiltonian dynamics. |
Table des matières
1 | |
Calculus on Manifolds | 60 |
ANALYTICAL DYNAMICS 1 59 | 159 |
Chapter 8 | 207 |
3 | 248 |
Hamiltonian Systems with Symmetry | 253 |
2 | 292 |
8 | 304 |
A Zoo of Stable Bifurcations | 595 |
The General Pathology | 606 |
The TwoBody Problem | 619 |
The Delaunay Variables | 631 |
Whittakers Method | 638 |
Poincare Variables | 647 |
Exercise | 656 |
The ThreeBody Problem | 663 |
0 | 341 |
2 | 357 |
HamiltonJacobi Theory and Mathematical Physics | 370 |
AN OUTLINE OF QUALITATIVE DYNAMICS | 507 |
Ditlerentiable Dynamics | 520 |
Hamiltonian Dynamics | 572 |
Exercises | 579 |
Exercises | 587 |
Exercises | 673 |
Exercises | 687 |
Exercises | 699 |
Blbllography | 759 |
791 | |
Glossary of Symbols | 807 |
Autres éditions - Tout afficher
Expressions et termes fréquents
action of G assume bifurcation called canonical transformation chart classical closed orbit commutes compact complete condition constant contact manifold corresponding critical point defined Definition denote derivative differential dimension eigenvalue elliptic energy surface equations equivalent equivariant ergodic example Exercise fiber finite-dimensional Flgure flow formula function geodesic given Hamiltonian system Hamiltonian vector field Hence Hilbert space homeomorphic identity induced inner product integral curve invariant isomorphism isotropic Lagrangian submanifold left-invariant Lemma Let F Let G Lie algebra Lie group linear map Marsden mechanics momentum mapping motion neighborhood nondegenerate one-form one-parameter open set operator orbit cylinder periodic orbits Poincare Proposition prove quantization regular value relation result Riemannian manifold Riemannian metric Sect smooth stability subgroup subset subspace Suppose surjective symmetric symplectic diffeomorphism symplectic form symplectic manifold symplectic structure tensor theorem theory topology unique vector bundle vector space Weinstein zero