应用动能定理进行多自由度系统建模探析

Analysis on Multi-Degree-of-Freedom(MDOF)System Modeling with the Kinetic Energy Theorem

探讨独立应用动能定理建立多自由度系统动力学方程的方法及其理论依据,证明了对于定常完整的理想约束系统,当动能表达式中不显含广义坐标时,将微分形式动能定理简化为广义坐标微分的和式方程,并令广义坐标微分前的系数为零,所得结果与拉格朗日方程所得结果一致。同时举例说明了这种方法的局限性,详细讨论了动能定理的适用性问题。

We discuss the methods of and theoretical basis for establishing kinetic equations of multi-degree-of-freedom(MDOF)systems by applying the kinetic energy theorem independently.We prove that with respect to dynamical systems with scleronomous,holonomic and ideal constraints,the result of the kinetic energy theorem with differential forms is equivalent to that of the Lagrange equation under the condition of not containing generalized coordinates in the expression for kinetic energy when the coefficient before the generalized coordinate differential is set zero.Meanwhile,the limitation of the kinetic energy theorem is illustrated by examples,and its applicability is discussed in detail.