CAJ | 학술논문

研究弱非完整系统Lagrange方程的Mei对称性导致的一种结构方程和新型精确以及近似守恒量.首先建立系统的Lagrange方程.其次在群的无限小变换下,给出了弱非完整系统及其一次近似系统Mei对称性的定义和判据,然后得到了Mei对称性导致的新型结构方程、新型精确和近似守恒量的表达式.最后,举例研究系统的精确新型守恒量和近似新型守恒量问题.
연구약비완정계통Lagrange방정적Mei대칭성도치적일충결구방정화신형정학이급근사수항량.수선건립계통적Lagrange방정.기차재군적무한소변환하,급출료약비완정계통급기일차근사계통Mei대칭성적정의화판거,연후득도료Mei대칭성도치적신형결구방정、신형정학화근사수항량적표체식.최후,거례연구계통적정학신형수항량화근사신형수항량문제.
@@@@A type of structural equation, new exact and approximate conserved quantity which are deduced from Mei symmetry of Lagrange equations for a weakly nonholonomic system, are investigated. First, Lagrange equations of weakly nonholonomic system are estab-lished. Next, under the infinitesimal transformations of Lie groups, the definition and the criterion of Mei symmetry for Lagrange equations in weakly nonholonomic systems and its first-degree approximate holonomic system are given. And then, the expressions of new structural equation and new exact and approximate conserved quantities of Mei symmetry for Lagrange equations in weakly nonholonomic systems are obtained. Finelly, an example is given to study the question of the exact and the approximate new conserved quantities.