Geometric Mechanics
Geometric Mechanics here means mechanics on a pseudo-riemannian manifold and the main goal is the study of some mechanical models and concepts, with emphasis on the intrinsic and geometric aspects arising in classical problems. The first seven chapters are written in the spirit of Newtonian Mechanic...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
2002, 2002
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| Edition: | 1st ed. 2002 |
| Series: | Lecture Notes in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- Introduction
- Differentiable manifolds
- Vector fields, differential forms and tensor fields
- Pseudo-riemannian manifolds
- Newtonian mechanics
- Mechanical systems on riemannian manifolds
- Mechanical Systems with non-holonomic constraints
- Hyperbolicity and Anosov systems
- Vakonomic mechanics
- Special relativity
- General relativity
- Appendix A: Hamiltonian and Lagrangian formalism
- Appendix B: Möbius transformations and the Lorentz group
- Appendix C: Quasi-Maxwell equations
- Appendix D: Viscosity solutions and Aubry-Mather theory