时空中的五维切向量：III。一些应用
Five-Dimensional Tangent Vectors in Space-Time: III. Some Applications
摘要：
在本系列的这一部分中，我将展示如何使用五张量来描述平坦时空中的有限和无穷小庞加莱变换。作为一个例子，我重新制定了经典力学的一个完美的刚体在三维欧氏空间的五个向量的类似物。然后，我介绍的标量，四矢量和四张量场在平坦的时空中的双矢量导数的概念，并计算其模拟在三维欧几里德空间的拉格朗日函数的几个点粒子在经典非相对论力学系统。
英文摘要：
In this part of the series I show how five-tensors can be used for describing in a coordinate-independent way finite and infinitesimal Poincare transformations in flat space-time. As an illustration, I reformulate the classical mechanics of a perfectly rigid body in terms of the analogs of five-vectors in three-dimensional Euclidean space. I then introduce the notion of the bivector derivative for scalar, four-vector and four-tensor fields in flat space-time and calculate its analog in three-dimensional Euclidean space for the Lagrange function of a system of several point particles in classical nonrelativistic mechanics.
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