复杂约束多体系统显式动力学表示及其应用

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中图分类号：0313.7 文献标志码：A

Abstract：The UDWADIA-KALABA equations provide an explicit solution method for complex constrained multi-body systems.This method can decouple the generalized acceleration and the generalized constraint force in the system without introducing auxiliary variables，and then obtain the generalized constraint force and generalized acceleration of the explicit expression.However，in the expression of the equation，the mass matrix is required to be positive definite，which is not suitable for dynamic systems with singular problems such as singular mass matrices，singular configurations and redundant constraints.For this reason，some experts and scholars deform the U-K equations by introducing auxiliary systems，which makes the actual multi-body system possess the same dynamic characteristics as the multi-body system with auxiliary system，so that singular problems can be well solved.Several methods of introducing auxiliary systems to modifythe basic U-K equations are discussed in detail，and the general process of modeling and solving complex constrained multi-body systems using U-K equation is given.Two examples with singular mass matrices are solved by using U-K equations and its modified methods.

Key words：U-K equation； complex multi-body system； singular problem； redundant constraint； explicitequation of motion

分析力学（即拉格朗日力学）是对经典力学的一种高度数学化的表示。（剩余9442字）