弹性力学辛体系广义动量矩定理  

THEOREM OF GENERALIZED MOMENTUM MOMENT IN SYMPLECTIC SYSTEM OF ELASTICITY

作　　者：朱炳麒[1] 卓家寿[2] 周建方[1] 

机构地区：[1]河海大学机电工程学院,江苏常州213022 [2]河海大学土木工程学院,江苏南京210098

出　　处：《工程力学》2010年第4期13-18,共6页Engineering Mechanics

摘　　要：类似于动力学中动量矩的概念,提出了弹性力学辛体系中广义动量矩的概念,给出了平面直角坐标辛体系和极坐标辛体系中广义动量、广义动量矩的统一定义,对广义动量矩的相关理论进行了研究。由Hamilton对偶方程导出了广义动量矩定理,得到了广义动量矩的守恒律,给出了守恒条件,分析了广义动量矩定理和守恒律的物理意义,经典问题验证了广义动量矩定理和守恒律。这一定理进一步丰富了弹性力学辛体系理论的内容,它和Hamilton函数、广义动量等相关理论一起,形成了辛体系中类似于动力学基本定理的一个理论体系。Analogous to the concept of momentum moment moment is presented in symplectie system of elasticity. The in dynamics, the concept of generalized momentum uniform definitions of generalized momentum and generalized momentum moment are given in symplectic system, which includes rectangular coordinate symplectic system and polar coordinate symplectic system. Some theorems corresponding to generalized momentum moment are studied. The theorem of generalized momentum conservation law of generalized momentum moment moment is deduced from Hamilton＇s dual equations. The is obtained, and the conservation condition is given. The physic meaning of the theorem is analyzed. The theorem is verified with some classic problems of elasticity. The theory in symplectic system of elasticity is enriched farther. Consequently, a theory system is formed which is similar to three basic theorems in dynamics. The system consists of three theorems corresponding to three physical quantities, i.e. generalized momentum, generalized momentum moment and Hamiltonian function.

关 键 词：弹性力学 辛体系 Hamilton对偶方程 广义动量 广义动量矩 广义动量矩定理 守恒律 

分 类 号：O343[理学—固体力学]