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经典力学导论:从变分法到最优控制(影印版)
本书是经典力学领域的经典著作,预备知识要求极低,仅需基础微积分和本科基础物理学知识,因此适合本科到研究生入门阶段的课程使用,也适合数学、物理和工程专业的学生群体。This is an intuitively motivated presentation ofmany topics in classical mechanics and related areas of control theory and calculus of variations. All topics throughout the book are treated with zero tolerance for unrevealing definitions and for proofs which leave the reader in the dark. Some areas of particular interest are: an extremely short derivation of the ellipticity of planetary orbits; a statement and an explanation of the “tennis racket paradox”; a heuristic explanation (and a rigorous treatment) of the gyroscopic effect; a revealing equivalence between thedynamics of a particle and statics of a spring; a short geometrical explanation of Pontryagin’s Maximum Principle, and more. In the last chapter, aimed at more advanced readers, the Hamiltonian and the momentum are compared to forces in a certain static problem. This gives a palpable physical meaning to some seemingly abstract concepts and theorems.
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