Geometric Mechanics

Waldyr Muniz Oliva (Autor)

Buch | Softcover

XII, 276 Seiten

2002 | 2002
Springer Berlin (Verlag)
978-3-540-44242-4 (ISBN)

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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 Mechanics while the last two ones as well as two of the four appendices describe the foundations and some aspects of Special and General Relativity. All the material has a coordinate free presentation but, for the sake of motivation, many examples and exercises are included in order to exhibit the desirable flavor of physical applications.

- 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.

Erscheint lt. Verlag	23.10.2002
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XII, 276 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	434 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Dynamical Systems • General relativity • Geometric Mechanics • holonomic and non-holonomic systems • manifold • Mechanik • Special relativity
ISBN-10	3-540-44242-1 / 3540442421
ISBN-13	978-3-540-44242-4 / 9783540442424
Zustand	Neuware