LEADER 03442nam 22006615 450 001 9910144940703321 005 20251117003204.0 010 $a3-540-45795-X 024 7 $a10.1007/b84214 035 $a(CKB)1000000000233289 035 $a(SSID)ssj0000323482 035 $a(PQKBManifestationID)11259099 035 $a(PQKBTitleCode)TC0000323482 035 $a(PQKBWorkID)10300014 035 $a(PQKB)11643427 035 $a(DE-He213)978-3-540-45795-4 035 $a(MiAaPQ)EBC6281118 035 $a(MiAaPQ)EBC5584844 035 $a(Au-PeEL)EBL5584844 035 $a(OCoLC)1066184667 035 $a(PPN)155206605 035 $a(EXLCZ)991000000000233289 100 $a20121227d2002 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aGeometric Mechanics /$fby Waldyr Muniz Oliva 205 $a1st ed. 2002. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2002. 215 $a1 online resource (XII, 276 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1798 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a3-540-44242-1 320 $aIncludes bibliographical references (pages [259]-261) and index. 327 $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. 330 $aGeometric Mechanics here means mechanics on a pseudo-riemannian manifold and the main goal is the study of some mechanical models and concepts, with emphasis on the intrinsic and geometric aspects arising in classical problems. The first seven chapters are written in the spirit of Newtonian Mechanics while the last two ones as well as two of the four appendices describe the foundations and some aspects of Special and General Relativity. All the material has a coordinate free presentation but, for the sake of motivation, many examples and exercises are included in order to exhibit the desirable flavor of physical applications. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1798 606 $aMathematical physics 606 $aDynamics 606 $aErgodic theory 606 $aTheoretical, Mathematical and Computational Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19005 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 615 0$aMathematical physics. 615 0$aDynamics. 615 0$aErgodic theory. 615 14$aTheoretical, Mathematical and Computational Physics. 615 24$aDynamical Systems and Ergodic Theory. 676 $a531 700 $aOliva$b Waldyr M.$4aut$4http://id.loc.gov/vocabulary/relators/aut$058977 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910144940703321 996 $aGeometric mechanics$9376933 997 $aUNINA