| 書目名稱 | Mathematical Methods of Classical Mechanics | | 編輯 | V. I. Arnold | | 視頻video | http://file.papertrans.cn/627/626283/626283.mp4 | | 叢書名稱 | Graduate Texts in Mathematics | | 圖書封面 |  | | 描述 | Many different mathematical methods and concepts are used in classical mechanics: differential equations and phase ftows, smooth mappings and manifolds, Lie groups and Lie algebras, symplectic geometry and ergodic theory. Many modern mathematical theories arose from problems in mechanics and only later acquired that axiomatic-abstract form which makes them so hard to study. In this book we construct the mathematical apparatus of classical mechanics from the very beginning; thus, the reader is not assumed to have any previous knowledge beyond standard courses in analysis (differential and integral calculus, differential equations), geometry (vector spaces, vectors) and linear algebra (linear operators, quadratic forms). With the help of this apparatus, we examine all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the hamiltonian formalism. The author has tried to show the geometric, qualitative aspect of phenomena. In this respect the book is closer to courses in theoretical mechanics for theoretical physicists than to traditional courses in theoretical mechanics as taught by mathematicians. | | 出版日期 | Textbook 19781st edition | | 關(guān)鍵詞 | Hamiltonian; Lie; Mathematica; Newtonian mechanics; algebra; calculus; classical mechanics; differential eq | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4757-1693-1 | | isbn_ebook | 978-1-4757-1693-1Series ISSN 0072-5285 Series E-ISSN 2197-5612 | | issn_series | 0072-5285 | | copyright | Springer Science+Business Media New York 1978 |
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