LEADER 04500nam 22006255 450 001 9910254599103321 005 20200704055501.0 010 $a9783319441474 024 7 $a10.1007/978-3-319-44147-4 035 $a(CKB)3710000000891733 035 $a(DE-He213)978-3-319-44147-4 035 $a(MiAaPQ)EBC4714740 035 $a(PPN)196326052 035 $a(EXLCZ)993710000000891733 100 $a20161008d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aClassical Mechanics $eHamiltonian and Lagrangian Formalism /$fby Alexei Deriglazov 205 $a2nd ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XVI, 445 p. 53 illus.) 311 $a3-319-44146-9 311 $a3-319-44147-7 320 $aIncludes bibliographical references and index. 327 $aSketch of Lagrangian Formalism -- Hamiltonian Formalism -- Canonical Transformations of Two-Dimensional Phase Space -- Properties of Canonical Transformations -- Integral Invariants -- Some Mechanical Problems in a Geometric Setting -- Transformations, Symmetries and Noether Theorem -- Hamiltonian Formalism for Singular Theories -- Classical and Quantum Relativistic Mechanics of a Spinning Particle -- Index. 330 $aThe revised edition of this advanced text provides the reader with a solid grounding in the formalism of classical mechanics, underlying a number of powerful mathematical methods that are widely used in modern theoretical and mathematical physics. It reviews the fundamentals of Lagrangian and Hamiltonian mechanics, and goes on to cover related topics such as canonical transformations, integral invariants, potential motion in geometric setting, symmetries, the Noether theorem and systems with constraints. While in some cases the formalism is developed beyond the traditional level adopted in the standard textbooks on classical mechanics, only elementary mathematical methods are used in the exposition of the material. New material for the revised edition includes additional sections on the Euler-Lagrange equation, the Cartan two-form in Lagrangian theory, and Newtonian equations of motion in context of general relativity. Also new for this edition is the inclusion of problem sets and solutions to aid in the understanding of the material presented. The mathematical constructions involved are explicitly described and explained, so the book is a good starting point for the student new to this field. Where possible, intuitive motivations are replaced by explicit proofs and direct computations, preserving the level of rigor that makes the book useful for more advanced students intending to work in one of the branches of the vast field of theoretical physics. To illustrate how classical-mechanics formalism works in other branches of theoretical physics, examples related to electrodynamics, as well as to relativistic and quantum mechanics, are included. 606 $aMechanics 606 $aMathematical physics 606 $aMechanics, Applied 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aClassical Mechanics$3https://scigraph.springernature.com/ontologies/product-market-codes/P21018 606 $aTheoretical, Mathematical and Computational Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19005 606 $aSolid Mechanics$3https://scigraph.springernature.com/ontologies/product-market-codes/T15010 606 $aApplications of Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M13003 606 $aMathematical and Computational Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/T11006 615 0$aMechanics. 615 0$aMathematical physics. 615 0$aMechanics, Applied. 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 14$aClassical Mechanics. 615 24$aTheoretical, Mathematical and Computational Physics. 615 24$aSolid Mechanics. 615 24$aApplications of Mathematics. 615 24$aMathematical and Computational Engineering. 676 $a531 700 $aDeriglazov$b Alexei$4aut$4http://id.loc.gov/vocabulary/relators/aut$0818866 906 $aBOOK 912 $a9910254599103321 996 $aClassical Mechanics$92000197 997 $aUNINA