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空间力系平衡的充要条件为主矢R和主矩L_0均等于零。对于空间直角坐标系可得到六个独立平衡方程,其中三个为力投影式,三个为力矩式。实际计算时还可采用六个力矩式,或五个力矩式加一个力投影式,或四个力矩式加二个力投影式。要保证这三组平衡方程的独立性,必须加上一些限制条件。文献[1]运用矩阵理论阐述了保证空间力系平衡方程独立性的限制条件。我们认为,还可以更简单地通过平衡方程的线性无关来讨论平衡方程的独立性。为此,本文引进由力矩轴方向余弦以及沿力矩轴作用单位力的力矩系数所组成的行列式,来分析空间力系平衡方程独立性的限制条件。
Necessary and sufficient conditions for the balance of forces in the space dominate the principal R and the principal moments L_0 are equal to zero. For the Cartesian coordinate system, six independent equilibrium equations are obtained, of which three are force projection and three are moment. The actual calculation can also be used six torque, or five torque plus one force projection, or four torque plus two force projection. To ensure the independence of the three equilibrium equations, some restrictions must be added. Literature [1] uses the matrix theory to expound the constraints that guarantee the independence of equilibrium equations of space force system. In our opinion, it is also easier to discuss the independence of the equilibrium equation by balancing the linear independence of the equation. Therefore, this paper introduces the determinant of the independence of equilibrium equations of space force system by introducing the determinant composed of the cosine of the moment axis and the moment coefficient of unit force acting along the moment axis.