03300nmm a2200361 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002300139245010900162250001700271260005600288300004200344505041500386653002000801653002400821653002300845653002400868653002800892653003200920653004700952653002500999653005601024653001401080710003401094041001901128989003601147856007201183082000801255520167501263EB001266337EBX0100000000000000088092100000000000000.0cr|||||||||||||||||||||161103 ||| eng a97833194414741 aDeriglazov, Alexei00aClassical MechanicshElektronische RessourcebHamiltonian and Lagrangian Formalismcby Alexei Deriglazov a2nd ed. 2017 aChambSpringer International Publishingc2017, 2017 aXVI, 445 p. 53 illusbonline resource0 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 aSolid Mechanics aApplied mathematics aMechanics, Applied aClassical Mechanics aEngineering mathematics aApplications of Mathematics aMathematical and Computational Engineering aMathematical physics aTheoretical, Mathematical and Computational Physics aMechanics2 aSpringerLink (Online service)07aeng2ISO 639-2 bSpringeraSpringer eBooks 2005- uhttps://doi.org/10.1007/978-3-319-44147-4?nosfx=yxVerlag3Volltext0 a531 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