Analytical Mechanics

Analytical mechanics is the foundation of many areas of theoretical physics including quantum theory and statistical mechanics, and has wide-ranging applications in engineering and celestial mechanics. This introduction to the basic principles and methods of analytical mechanics covers Lagrangian and Hamiltonian dynamics, rigid bodies, small oscillations, canonical transformations and Hamilton-Jacobi theory. This fully up-to-date textbook includes detailed mathematical appendices and addresses a number of advanced topics, some of them of a geometric or topological character. These include Bertrand's theorem, proof that action is least, spontaneous symmetry breakdown, constrained Hamiltonian systems, non-integrability criteria, KAM theory, classical field theory, Lyapunov functions, geometric phases and Poisson manifolds. Providing worked examples, end-of-chapter problems, and discussion of ongoing research in the field, it is suitable for advanced undergraduate students and graduate students studying analytical mechanics.

分析力學是理論物理學中許多領域的基礎，包括量子理論和統計力學，並在工程學和天體力學中有廣泛的應用。這本介紹分析力學基本原理和方法的教科書涵蓋了拉格朗日動力學和哈密頓動力學、剛體、小振動、正準變換和哈密頓-雅可比理論。這本最新的教科書包含詳細的數學附錄，並涵蓋了一些具有幾何或拓撲特性的高級主題。這些主題包括Bertrand定理、最小作用量的證明、自發對稱破缺、受限哈密頓系統、不可積條件、KAM理論、經典場論、李雅普諾夫函數、幾何相位和泊松流形。本書提供了實例、章末問題和對該領域的研究討論，適合高年級本科生和攻讀分析力學的研究生使用。