标题： 关于物理系统的数学模型的一般结构 显示英文标题

标题： On the general structure of mathematical models for physical systems

摘要： 建议认为，基于基本原理（如守恒定律或平衡原理）的任何物理系统的数学模型都有一些共同的元素，即运动学状态空间、动力学状态空间、将动力学状态与运动学状态联系起来的本构关系以及对偶性原理。 运动方程或静力学随后通过一方面规定运动学状态的可积性，另一方面为动力学状态规定一个与其对偶的陈述而产生。 来自各种基本物理系统的事例被给出。 显示英文摘要

摘要： It is proposed that the mathematical models for any physical systems that are based in first principles, such as conservation laws or balance principles, have some common elements, namely, a space of kinematical states, a space of dynamical states, a constitutive law that associates dynamical states with kinematical states, as well as a duality principle. The equations of motion or statics then come about from, on the one hand, specifying the integrability of the kinematical state, and on the other hand, specifying a statement that is dual to it for the dynamical states. Examples are given from various fundamental physical systems.