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上一篇文章介绍的物质导数从微分的角度解释了运动中的流体微团随时间的变化率，这一篇将介绍 雷诺输运理论 （Reynolds Transport Theorem），它从积分型方程中的 控制体 的角度建立了这样的关系：一个控制体内物理量的变化率等于该控制体内物理量本身. Transport equation u_ {t}+\boldsymbol {b}\cdot\nabla u=0 in \mathbb {R}^ {n}\times (0,\infty) 这输运方程是最简单的一个 偏微分方程，对这问题的解决是使用所谓特征曲线法（method of characteristics）化为ODE，这个方法在ODEs中已经见过了——恰当方程组. a(t) 称为莱布尼茨公式。其中,a(t) 和b(t)分别为边界值,是时间的函数。式(1)等号左边表示积分函数对时间的导数;右边第一项积分为被积函数对时间偏导数的积分;第二项为上游边界运动引起的,其中db t dt Vu相当于上游边界速度;第三项为下游边界运动引起的.
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雷诺传输定理（Reynolds transport theorem），又称为传输方程式（Transport equation），是描述流体系统中物理量随控制容积变化的数学定理，由奥斯鲍恩·雷诺提出。 But it will be used almost exclusively in this course and is used generally in engineering analysis. Note that b need not be mounted (1.5) in a for b to have a simple angular velocity in a
This book is a revision of dynamics
Theory and applications by t It is used to recast time derivatives of integrated quantities and is useful in formulating the basic equations of continuum mechanics. This relation is also known as the reynold's transport theorem and is a generalization of the leibniz rule Theory and applications (1985), by t
Levinson, and presents the method for forming equations of motion by constructing generalized active forces and generalized inertia forces. We show in this section that the solution of the transport equation can be seen as the expectation of a random process The random process simulates the behavior of one particle in the medium. In this paper, it is shown how improvements in computational efficiency can be effected by using kane's dynamical equations to formulate explicit equations of motion.
Note that the above equation is approximate, so it may not always be accurate
