Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA.
Phys Rev Lett. 2013 Apr 26;110(17):174301. doi: 10.1103/PhysRevLett.110.174301. Epub 2013 Apr 22.
Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often goes unnoticed in physics: it is formulated as a boundary value problem in time but is used to derive equations of motion that are solved with initial data. This subtlety can have undesirable effects. I present a formulation of Hamilton's principle that is compatible with initial value problems. Remarkably, this leads to a natural formulation for the Lagrangian and Hamiltonian dynamics of generic nonconservative systems, thereby filling a long-standing gap in classical mechanics. Thus, dissipative effects, for example, can be studied with new tools that may have applications in a variety of disciplines. The new formalism is demonstrated by two examples of nonconservative systems: an object moving in a fluid with viscous drag forces and a harmonic oscillator coupled to a dissipative environment.
哈密顿作用量原理是理论物理的基础，并且在从纯数学到经济学等许多其他学科中都有应用。尽管它很有用，但哈密顿原理有一个微妙的陷阱，在物理学中常常被忽视：它是作为一个时间的边值问题来表述的，但却被用来推导出用初始数据求解的运动方程。这种微妙之处可能会产生不良影响。我提出了一种与初值问题兼容的哈密顿原理的表述方式。值得注意的是，这为非保守系统的拉格朗日和哈密顿动力学提供了一种自然的表述方式，从而填补了经典力学中的一个长期存在的空白。因此，例如，可以用可能在各种学科中有应用的新工具来研究耗散效应。新形式主义通过两个非保守系统的例子来演示：一个在粘性阻力的流体中运动的物体和一个与耗散环境耦合的谐振子。
