Mathematical aspects of classical and celestial mechanics
Mathematical aspects of classical and celestial mechanics
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DOI：
10.1007/978-3-540-48926-9
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发表时间：
1997-02
期刊：
影响因子：
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通讯作者：
V. Arnold;V. V. Kozlov-V.;A. Neishtadt
中科院分区：
文献类型：
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作者：
V. Arnold;V. V. Kozlov-V.;A. Neishtadt
在本书中，我们描述了经典力学的基本原理、问题和方法。我们主要关注该主题的数学方面。尽管这里考虑的模型的物理背景以及本书中研究的现象的应用方面的探讨程度要小得多，但我们试图阐明？首先也是最重要的是经典力学的“工作”装置。该装置主要包含在第 1、3、5、6 和 8 章中。第 1 章专门介绍经典力学的基本数学模型，这些模型通常用于描述实际机械系统的运动。特别关注有约束的运动的研究以及动力学中约束的实现问题。在第三章中，我们讨论机械系统的对称群和相应的守恒定律。我们还阐述了对称系统的阶数约简理论的各个方面，该理论在应用中经常使用。第4章专门介绍经典力学的变分原理和方法。特别是，它们允许人们获得有关周期性轨迹存在性的重要结果。特别注意可能运动的区域具有非空边界的情况。指出了变分法在运动稳定性理论中的应用。
In this book we describe the basic principles, problems, and methods of cl-sical mechanics. Our main attention is devoted to the mathematical side of the subject. Although the physical background of the models considered here and the applied aspects of the phenomena studied in this book are explored to a considerably lesser extent, we have tried to set forth? rst and foremost the “working” apparatus of classical mechanics. This apparatus is contained mainly in Chapters 1, 3, 5, 6, and 8. Chapter 1 is devoted to the basic mathematical models of classical-chanics that are usually used for describing the motion of real mechanical systems. Special attention is given to the study of motion with constraints and to the problems of realization of constraints in dynamics. In Chapter 3 we discuss symmetry groups of mechanical systems and the corresponding conservation laws. We also expound various aspects of ord-reduction theory for systems with symmetries, which is often used in appli-tions. Chapter 4 is devoted to variational principles and methods of classical mechanics. They allow one, in particular, to obtain non-trivial results on the existence of periodic trajectories. Special attention is given to the case where the region of possible motion has a non-empty boundary. Applications of the variational methods to the theory of stability of motion are indicated.