连续介质概念的另一种选择
An alternative to the concept of continuous medium
摘要：
离散力学提出了力学方程的另一种表述，其中Navier-Stokes方程和Navier-Lamé方程成为离散运动方程的近似。它通过将这些方程的应用领域扩展到所有空间和时间尺度来统一流体力学和固体力学领域。本文介绍了放弃连续介质和全球参照系概念所导致的本质区别。通过流体和固体观测证实的连续介质力学的结果是没有疑问的。连续介质的概念并没有失效，提出的离散公式只是拓宽了经典方程的应用范围。离散的运动方程引入了几个重要的修改，特别是体积元素上的动力学基本定律变成了边缘上的加速度守恒定律。加速度被认为是一个绝对量被写为两个分量的总和，一个soledoidal的其他无旋根据当地正交亥姆霍兹-霍奇分解。质量被抛弃，并由加速度的标量势和矢量势所表示的压缩能和旋转能代替。运动方程和所有的物理参数只用长度和时间这两个基本单位来表示。这两种方法之间的本质区别被列出，其中一些进行了深入的讨论。对于已知的纳维-斯托克斯方程悖论或惯性对纳维-拉梅方程的重要性，情况尤其如此。
英文摘要：
Discrete mechanics proposes an alternative formulation of the equations of mechanics where the Navier-Stokes and Navier-Lamé equations become approximations of the equation of discrete motion. It unifies the fields of fluid and solid mechanics by extending the fields of application of these equations to all space and time scales. This article presents the essential differences induced by the abandonment of the notion of continuous medium and global frame of reference. The results of the mechanics of continuous medium validated by fluid and solid observations are not questioned. The concept of continuous medium is not invalidated, the discrete formulation proposed simply widens the spectrum of the applications of the classical equations. The discrete equation of motion introduces several important modifications, in particular the fundamental law of the dynamics on an element of volume becomes a law of conservation of the accelerations on an edge. The acceleration considered as an absolute quantity is written as a sum of two components, one soledoidal the other irrotational according to a local orthogonal Helmholtz-Hodge decomposition. The mass is abandoned and replaced by the compression and rotation energies represented by the scalar and vectorial potentials of the acceleration. The equation of motion and all the physical parameters are expressed only with two fundamental units, those of length and time. The essential differences between the two approaches are listed and some of them are discussed in depth. This is particularly the case with the known paradoxes of the Navier-Stokes equation or the importance of inertia for the Navier-Lamé equation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
