Symmetry in Mechanics: A Gentle, Modern Introduction
Autor Stephanie Frank Singeren Limba Engleză Paperback – mar 2001
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Specificații
ISBN-13: 9780817641450
ISBN-10: 0817641459
Pagini: 193
Ilustrații: XII, 193 p. 4 illus.
Dimensiuni: 155 x 235 x 12 mm
Greutate: 0.37 kg
Ediția:2004
Editura: Birkhäuser Boston
Colecția Birkhäuser
Locul publicării:Boston, MA, United States
ISBN-10: 0817641459
Pagini: 193
Ilustrații: XII, 193 p. 4 illus.
Dimensiuni: 155 x 235 x 12 mm
Greutate: 0.37 kg
Ediția:2004
Editura: Birkhäuser Boston
Colecția Birkhäuser
Locul publicării:Boston, MA, United States
Public țintă
ResearchCuprins
0 Preliminaries.- 1 The Two-Body Problem.- 2 Phase Spaces are Symplectic Manifolds.- 3 Differential Geometry.- 4 Total Energy Functions are Hamiltonian Functions.- 5 Symmetries are Lie Group Actions.- 6 Infinitesimal Symmetries are Lie Algebras.- 7 Conserved Quantities are Momentum Maps.- 8 Reduction and The Two-Body Problem.- Recommended Reading.- Solutions.- References.
Recenzii
"Symmetry in Mechanics is directed to students at the undergraduate level and beyond, and offers a lovely presentation of the subject . . . The first chapter presents a standard derivation of the equations for two-body planetary motion. Kepler's laws are then obtained and the rule of conservation laws is emphasized. . . . Singer uses this example from classical physics throughout the book as a vehicle for explaining the concepts of differential geometry and for illustrating their use. These ideas and techniques will allow the reader to understand advanced texts and research literature in which considerably more difficult problems are treated and solved by identical or related methods. The book contains 122 student exercises, many of which are solved in an appendix. The solutions, especially, are valuable for showing how a mathematician approaches and solves specific problems. Using this presentation, the book removes some of the language barriers that divide the worlds of mathematics and physics."
—Physics Today
"This is a very interesting book. Those educated in traditional mechanics will acquire [from reading it] knowledge of modern mathematics hidden beyond traditional concepts in the realm of celestial mechanics, [and] . . . pure mathematicians will understand how their discipline enters into practical problems. The author shows how fundamental concepts of symplectic geometry implicitly occur in mechanics . . . the mathematical presentation is ingenious and subtle. There are a lot of exercises for the reader and the solutions of most of them are given in a separate chapter. I can highly recommend this book to undergraduate and PhD students . . . it is ideally suited for teaching a course on the subject."
—Mathematical Reviews
—Physics Today
"This is a very interesting book. Those educated in traditional mechanics will acquire [from reading it] knowledge of modern mathematics hidden beyond traditional concepts in the realm of celestial mechanics, [and] . . . pure mathematicians will understand how their discipline enters into practical problems. The author shows how fundamental concepts of symplectic geometry implicitly occur in mechanics . . . the mathematical presentation is ingenious and subtle. There are a lot of exercises for the reader and the solutions of most of them are given in a separate chapter. I can highly recommend this book to undergraduate and PhD students . . . it is ideally suited for teaching a course on the subject."
—Mathematical Reviews