最小作用量原理与哈密顿方程.docx

最小作用量原理与哈密顿方程 摘要 本文通过对最小作用量原理历史发展过程的分析，展示了科学研究中追求简单 性、统一性的科学理性精神，以及这一原理对整个物理学的发展所具有的重大认识论 和方法论价值。结合哈密顿原理与最小作用量原理的发展，解释哈密顿原理,给出了 哈密顿正则方程及相关结论,即广义动量守恒,机械能量守恒等。 讨论了哈密顿积分的条件。对保守系统,非保守系统的H— J方程给出了解决关 于力学问题的步骤。对牛顿经典力学中的力学问题进行了分析，并用最小作用量原理 对其进行了重新定义与解答。从以下几个方面提出了一些自己的看法：（1）最小作用 量原理的提出；（2）作用量的概念；（3）变分法与分析力学；（4）对最小作用量原理 的讨论 最小作用量原理的有效性远远超出了有质物体的力学范围。在这种意义上，它是 关于自然界中一切可逆过程的普遍定理可以说，作为我们探求新现象的物理规律时的 一个有启发性的原理和向导，这一原理具有很高的价值。 关键字：哈密顿原理，最小作用量原理作用量，经历量，广义哈密顿原理，动 力学 PAGE PAGE # ABSTRACT Based on the least action principle analysis of the process of historical development, demonstrates the scientific research in the pursuit of simplicity, unity of science and rational spirit, as well as the principle for the development of the whole physics is the important value of epistemology and methodology. Combining with the HamiltonfS principle and the development of the least action principle, explain the Hamilton,s principle, Hamilton canonical equation and the relevant conclusions are given, namely generalized momentum conservation, conservation of mechanical energy, etc. The conditions of the Hamiltonian integral is discussed. On the conservative system, the equation of conservative system H-J steps to solve the problem of about mechanics. Of Newtonian mechanics in the classical mechanics problems are analyzed, and the least action principle to redefine and solutions. Put forward some own views from the following several aspects: (1) the least action principle is put forward; (2) the concept of action; (3) the variational method and analytical mechanics; (4) the discussion of the least action principle The effectiveness of the least action principle goes far beyond the scope of the mechanics of a qualitative objects. Is in this sense, it,s all about the nature of the reversible process general theorem, so to speak, as we explore the new phenomenon of physical laws of an instructive principle and guide, this principle has the very high value. Key words: Hamilton,s principle, the princ