单面非Chetaev型非完整系统的积分因子和守恒律

Integrating Factors and Conservation Laws for Mechanical Systems with Non-Chetaev Nonholonomic Unilateral Constraints

为了进一步研究非完整系统的守恒律,将积分因子方法应用于具有单面约束的非Chetaev型非完整系统,建立了寻找具有单面约束的非Chetaev型非完整系统的守恒律的一种新方法。首先寻求非完整系统存在守恒律的必要条件;其次建立系统积分因子与守恒律的关系,给出用于确定积分因子的广义Killing方程;最后得到单面非Chetaev型非完整系统的守恒律,并举例说明结果的应用。结果表明利用积分因子方法可以研究单面非Chetaev型非完整系统的守恒律。

In order to further study the conservation laws of nonholonomic mechanical systems,the meth-od of integrating factors is applied to mechanical systems with non-Chetaev nonholonomic unilateral con-straints,which establishes a new method to find the conservation laws of mechanical systems with non-Chetaev nonholonomic unilateral constraints.Firstly,the necessary conditions for the existence of the conservation laws of nonholonomic mechanical systems are studied.Secondly,the relation between the conservation laws and the integrating factors is established,then the generalized Killing equations which are used to determine the integrating factors can be presented.Finally,the conservation laws of non-Che-taev nonholonomic mechanical systems with unilateral constraints can be found.Also,an example is giv-en to illustrate the application of the results.The results show that the method of integrating factors can be used to study the conservation laws of mechanical systems with non-Chetaev nonholonomic unilateral con-straints.