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Classical Mechanics: Hamiltonian and Lagrangian Formalism-P2P

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The revised edition of this advanced textbook 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.

Classical Mechanics: Hamiltonian and Lagrangian Formalism-P2P
2016 | 445 pages | PDF | 7.10 MB


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  1. 这本高级教科书的修订本使读者在经典力学体系方面打下坚实基础, 在现代理论和数学物理学中广泛应用了许多有效的数学方法。本书回顾了拉格朗日和哈密顿力学的基本原理, 并讨论了相关主题, 如规范变换、积分不变量、几何设置中的势运动、对称、诺特定理和具有约束的系统。 本修订版新增的内容包括欧拉-拉格朗日方程、拉格朗日理论中的Cartan two-form, 以及广义相对中的牛顿运动方程。
    sunsource(特殊组-翻译)8个月前 (04-30)