LEADER 04666nam 22007215 450 001 9910734832003321 005 20231023125235.0 010 $a3-031-27612-4 024 7 $a10.1007/978-3-031-27612-5 035 $a(MiAaPQ)EBC7254943 035 $a(Au-PeEL)EBL7254943 035 $a(OCoLC)1381095723 035 $a(DE-He213)978-3-031-27612-5 035 $a(BIP)087962843 035 $a(PPN)270613056 035 $a(CKB)26815436900041 035 $a(EXLCZ)9926815436900041 100 $a20230531d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAnalytical Mechanics $eClassical, Lagrangian and Hamiltonian Mechanics, Stability Theory, Special Relativity /$fby Valter Moretti 205 $a1st ed. 2023. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2023. 215 $a1 online resource (848 pages) 225 1 $aLa Matematica per il 3+2,$x2038-5757 ;$v150 311 08$aPrint version: Moretti, Valter Analytical Mechanics Cham : Springer,c2023 9783031276118 320 $aIncludes bibliographical references and index. 327 $a1 The Space and Time of Classical Physics -- 2 The Spacetime of Classical Physics and Classical Kinematics -- 3 Newtonian dynamics: a conceptual critical review -- 4 Balance equations and first integrals in Mechanics -- 5 Introduction to Rigid Body Mechanics -- 6 Introduction to stability theory with applications to Mechanics -- 7 Foundations of Lagrangian Mechanics -- 8 Symmetries and conservation laws in Lagrangian Mechanics -- 9 Advanced topics in Lagrangian Mechanics -- 10 Mathematical introduction to Special Relativity and the relativistic Lagrangian formulation -- 11 Fundamentals of Hamiltonian Mechanic -- 12 Canonical Hamiltonian theory, Hamiltonian symmetries and Hamilton-Jacobi theory -- 13 Hamiltonian symplectic structures: an introduction -- 14 Complement: elements of the theory of ordinary differential equations -- 15 Complement: the physical principles at the foundations of Special Relativity -- Appendix A: elements of Topology, Analysis, Linear Algebra and Geometry -- Appendix B: advanced topics in Differential Geometry -- Appendix C: Solutions and/or hints to suggested exercises. 330 $aThis textbook aims at introducing readers, primarily students enrolled in undergraduate Mathematics or Physics courses, to the topics and methods of classical Mathematical Physics, including Classical Mechanics, its Lagrangian and Hamiltonian formulations, Lyapunov stability, plus the Liouville theorem and the Poincaré recurrence theorem among others. The material also rigorously covers the theory of Special Relativity. The logical-mathematical structure of the physical theories of concern is introduced in an axiomatic way, starting from a limited number of physical assumptions. Special attention is paid to themes with a major impact on Theoretical and Mathematical Physics beyond Analytical Mechanics, such as the Galilean symmetry of classical Dynamics and the Poincaré symmetry of relativistic Dynamics, the far-fetching relationship between symmetries and constants of motion, the coordinate-free nature of the underpinning mathematical objects, or the possibility of describing Dynamics in a global way while still working in local coordinates. Based on the author?s established teaching experience, the text was conceived to be flexible and thus adapt to different curricula and to the needs of a wide range of students and instructors. 410 0$aLa Matematica per il 3+2,$x2038-5757 ;$v150 606 $aMathematics 606 $aMechanics, Applied 606 $aMechanics 606 $aMathematical physics 606 $aMathematics 606 $aEngineering Mechanics 606 $aClassical Mechanics 606 $aTheoretical, Mathematical and Computational Physics 606 $aMecànica analítica$2thub 608 $aLlibres electrònics$2thub 610 $aMathematics 615 0$aMathematics. 615 0$aMechanics, Applied. 615 0$aMechanics. 615 0$aMathematical physics. 615 14$aMathematics. 615 24$aEngineering Mechanics. 615 24$aClassical Mechanics. 615 24$aTheoretical, Mathematical and Computational Physics. 615 7$aMecànica analítica 676 $a531.01515 700 $aMoretti$b Valter$0721877 702 $aChiossi$b Simon G. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910734832003321 996 $aAnalytical mechanics$93554376 997 $aUNINA