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001 978-3-540-45795-4
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008 121227s2002 gw | s |||| 0|eng d
020 _a9783540457954
_9978-3-540-45795-4
024 7 _a10.1007/b84214
_2doi
050 4 _aQC19.2-20.85
072 7 _aPHU
_2bicssc
072 7 _aSCI040000
_2bisacsh
072 7 _aPHU
_2thema
082 0 4 _a530.1
_223
100 1 _aMuniz Oliva, Waldyr.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aGeometric Mechanics
_h[electronic resource] /
_cby Waldyr Muniz Oliva.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2002.
300 _aXII, 276 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1798
505 0 _aIntroduction -- 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.
520 _aGeometric 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.
650 0 _aDifferentiable dynamical systems.
650 1 4 _aTheoretical, Mathematical and Computational Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19005
650 2 4 _aDynamical Systems and Ergodic Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M1204X
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540442424
776 0 8 _iPrinted edition:
_z9783662162538
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1798
856 4 0 _uhttps://doi.org/10.1007/b84214
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c11263
_d11263