论微分约束系统的d-δ对易关系  

On d-δ commutation relation of constrained differential systems

作　　者：郭永新[1] 赵喆[2] 刘世兴[1] 刘畅[1] 

机构地区：[1]辽宁大学物理学院和数学应用中心,沈阳110036 [2]沈阳药科大学基础学院,沈阳110016

出　　处：《物理学报》2008年第3期1301-1306,共6页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:10472040);辽宁省优秀青年科研人才培养基金(批准号:3040005);教育部留学回国人员科研启动基金(批准号:2004527);教育部春晖计划项目(批准号:Z2005-1-21006);辽宁省教育厅基础研究计划项目(批准号:05L155)资助的课题~~

摘　　要：利用Frobenius可积性定理,研究微分约束系统一个重要的变分法问题:微分运算与变分运算的对易关系.文中以微分约束的Frobenius可积性理论为依据,在分析线性稳定微分约束系统和仿射微分约束系统的d-δ对易关系基础上,简要论证了微分与变分的非对易子与微分约束的非完整性之间的关系.对非线性微分约束系统的微分与变分运算的对易关系作了讨论.给出了三个实例来验证结论.An important problem of calculus of variations used in constrained differential systems, i.e. , the commutation relation of differential operator and variational oprerator, is investigated by means of Frobenius theorem of integrability. Based on analyzing the d-δ commutation relation for the linear stationay differential constrained systems and affine differential constrained systems, the relationship between noncommutator of differentiation and variation and nonholonomicity of the differential constraints is briefly proved by means of Frobenius integrability theory. The commutation relation for non-linear differential constrained systems is also discussed in the paper. Finally, three examples are given to verify the results.

关 键 词：非完整约束 Frobenius可积性 d-δ对易关系 线性稳定微分约束系统 仿射微分约束系统 

分 类 号：O316[理学—一般力学与力学基础]