空间力系三、四、五、六力矩平衡方程最简形式与矩阵判据

The Simplest Forms of Three, Four, Five and Six Moment Equilibrium Equations in Three Dimensional Force Systems and theMatrix Criteria

本文对空间力系平衡方程式的三、四、五、六力矩式中给出了其最简形式并提出了判别矩轴、投影轴是否独立的统一矩阵判据,该判据适用于理力计算机分析。根据矩阵判据最简的原则证明了所给诸力矩式确为众多的复杂的三、四、五、六力矩式中的最简形式,并利用最简的五、六力矩式导出了平面力系的二、三力矩式,弥补了静力学体系的一个缺陷。最后利用最简六力矩式导出了Appell结果。

The simplest forms of all possible three, four, five and six moment equilibrium equat ions are derived in this paper.The results are succint and good in regularity, which can be applied to teach students. The restrictive condition matrix is also presented, which can be a general criteria to judge the suitability of the projection axes and the axes of moment selected. The matrix criteria can be used in all computers for statics and dynamics analysis in theoretical mechanics. The three, four, five and six moment equilibrium equations are proved respectively to be really the simplest form according to the principle that the restrictive condition matrix is the simplest form, and the two,three moment equilibrium equations of planar force systems are derived by utilizing the simplest forms of five, six moment respect ively, which remedy a deficit of statics system. Appell's results are derived also by utilizing the simplest six moment equilibrium equations.