Classical Mechanics Is Lagrangian; It Is Not Hamiltonian
Classical Mechanics Is Lagrangian; It Is Not Hamiltonian
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DOI：
10.1093/bjps/axs034
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发表时间：
2014-06-01
影响因子：
3.4
通讯作者：
Curiel, Erik
中科院分区：
文献类型：
--
作者：
Curiel, Erik
人们可以（在大多数情况下）在拉格朗日或哈密顿框架中制定经典系统的模型。虽然人们通常认为这两种表述在所有重要方面都是等价的，但事实并非如此：人们用来表述每一种理论的基本几何结构并不同构。这就提出了一个问题，即两者之一是否是表示经典系统的更自然的框架。在这种情况下，答案是肯定的：我的状态和草图证明两个技术成果的启发简单的物理参数的一般性质的经典系统的效果，在精确的意义上，经典系统恰恰表明几何结构拉格朗日力学提供的表示系统，并没有提供汉密尔顿。这一论证不仅阐明了两个力学体系的概念结构，而且阐明了它们之间的关系以及它们各自代表物理系统的机制。这也说明了为什么对物理理论的表征内容采用简单的结构方法是行不通的。
One can (for the most part) formulate a model of a classical system in either the Lagrangian or the Hamiltonian framework. Though it is often thought that those two formulations are equivalent in all important ways, this is not true: the underlying geometrical structures one uses to formulate each theory are not isomorphic. This raises the question of whether one of the two is a more natural framework for the representation of classical systems. In the event, the answer is yes: I state and sketch proofs of two technical results-inspired by simple physical arguments about the generic properties of classical systems-to the effect that, in a precise sense, classical systems evince exactly the geometric structure Lagrangian mechanics provides for the representation of systems, and none provided by Hamiltonian. The argument not only clarifies the conceptual structure of the two systems of mechanics, but also their relations to each other and their respective mechanisms for representing physical systems. It also shows why naively structural approaches to the representational content of physical theories cannot work.