基于Udwadia-Kalaba理论的Hamel嵌入法研究

Hamel嵌入法直接将约束嵌入到非约束运动的动能中去，从而避免使用Lagrange(拉格朗日)乘子.但这个简单、直观的方法却并不总是正确.Hamel认为这种方法可能导致错误的结果，然而他并没有给出Hamel嵌入法正确性的适用条件.在利用Udwadia Kalaba理论的基础上，提出了Hamel嵌入法成立的充要条件；指出了Rosenberg在Hamel嵌入法正确性研究中的不足，通过给出的具体算例可以看出，在完整约束下Hamel嵌入法可能不正确，而在非完整约束下也可能得出正确的结果；理论和实例分析表明，Hamel嵌入法是否成立除了与约束有关以外还与系统模型相关.

Study on Hamel's Embedding Method via the Udwadia-Kalaba Theory

Hamel embedded the constraint directly into the kinetic energy of unconstrained motion to avoid the use of Lagrange multiplier,which made a simple,straightforward,but incompletely correct method.Hamel stated that this method may lead to wrong results,but did not point out the applicable conditions for its correctness.Based on the Udwadia-Kalaba theory,the necessary and sufficient condition for Hamel's embedding method was found.Besides,examples show that Rosenberg's work on the validity of Hamel's embedding method is insufficient.Hamel's embedding method may be correct under nonholonomic constraint and may be incorrect under holonomic constraint.According to the theoretical and exemplary analysis,the correctness of Hamel's embedding method is not only determined by the constraints,but also determined by the mechanical system model.