论文标题
修订维度分析的代数基础
An Algebraic Foundation of Amended Dimensional Analysis
论文作者
论文摘要
我们基于通用代表定理，以实现协变标量表示，我们提出了一种尺寸分析的创新方法。该定理又以纯粹的数量空间代数理论为基础。给出了基于这种方法的维度分析的示例，表明它允许通过传统维度分析获得的结果得到加强。例如，可以在不使用运动方程的情况下得出两体系统的轨道周期。
We present an innovative approach to dimensional analysis, based on a general representation theorem for complete quantity functions admitting a covariant scalar representation; this theorem is in turn grounded in a purely algebraic theory of quantity spaces. Examples of dimensional analysis based on this approach are given, showing that it allows results obtained by traditional dimensional analysis to be strengthened. For example, the orbital period of a two-body system can be derived without use of equations of motion.
