关于离散系统的动力学方程

On the Dynamic Equation of Discrete System with Time-Variant Generalized Coordinate Transformation

本文对处于复杂运动中的离散系统的动力学方程进行了详细的推导,并讨论了在微幅运动假定下,方程线化后的形式。最终给出了一般意义上的非定常系统的动力学方程式的正确表达式。

In existing dynamic equation of discrete system, gyroscopic forces (or Co-riolis force) and circulatory forces (or constraint damping forces), not accoun-ted for in classical translational dynamic equation of discrete system, are intro-duced by Meirovitch [1]. But in Ref. [1], the resulting governing equationfrom Lagrangian did not consider the circumstance in which the generalizedcoordinate transformation u_s=u_s (q_1, q_2, …… q_f, t) is time-variant. Therefore,the equation will not be applicable to the system, for example, with unsteadyrotation-a well known very important practical requirement in engineering. After a detailed derivation, what the author did that was new was to pro-vide a set of dynamic equations of discrete system and its Iinearized form whichcan be applicable directly to the rheonomic constraint system (i.e in which thegeneralized coordinate transformation is time-variant). Although, a correct result can also be obtained from Lagrange's equationwith complete Lagrangian including the effects of time-variant u_s, it is clearthat this process makes practical application unnecessarily tedious. In comparison with Eq. (2.22) in Ref. [1], the proposed dynamic equationincludes two new terms: the first one in form of B^T. q which usually is rela-ted to the unsteady rotational movement and second term gengrally dependson time but not on generalized displacement or velocities.