摘要
目的研究具有二阶非完整约束的力学系统守恒律．方法利用Ｊｏｕｒｄａｉｎ变分原理∑Ｎｉ＝１（Ｆｉ－ｍｉｒ¨ｉ）·δ１ｒ．ｉ＝０，引入Ｊｏｕｒｄａｉｎ生成元（Δ１ｑｓ）．＝εＦｓ（ｔ，ｑ，ｑ．），（Δ１ｔ）．＝εｆ（ｔ，ｑ，ｑ．）和推广的Четаев定义∑ｎｓ＝１φβｑ¨ｓδ１ｑ．ｓ＝０，得到无限小变换下列的不变性条件．结果当无限小生成元ｆ，Ｆｓ满足一定条件时可得到系统的守恒律．结论推广了完整系统和一阶非完整系统的相应结果，二阶非完整系统也存在守恒律．
Aim\ To study the conservation laws of the mechanical systems with secondorder nonholonomic constraints Methods Using the Jourdain′s principle ∑Ni=1(F i-m i r ¨ i)·δ 1 r i=0,introducing the Jourdain′s generator (Δ 1q s) =εF s(t,[WTHX]q, q .),(Δ 1t) =εf(t,q, q .),and the generalized Chetaev′s definition ∑ns=1φ β q ¨ sδ 1 q s=0 to obtain the condition of invariance under the infinitesimal transformations Results If the generator f, F s satisfies some conditions, the conservation laws of the system can be obtained Conclusion The corresponding results of the holonomic systems and the systems with first order nonholonomic constraints are extended and the conservation laws of the systems with second order nonholonomic constraints exist also
出处
《北京理工大学学报》
EI
CAS
CSCD
1998年第1期17-21,共5页
Transactions of Beijing Institute of Technology
基金
国家自然科学基金
