一般力学广义变分原理的对偶形式

Dual form of generalized variational principles in general mechanics

应用对合变换,将一类变量变分原理的驻值条件变换为两类变量的基本方程.按照广义力和广义位移之间的对应关系,将各基本方程乘上相应的虚量,代数相加,然后积分,进而建立了完整系统和非完整系统两类变量广义变分原理的2种对偶形式.应用类似的方法,建立了完整系统和非完整系统三类变量广义变分原理的2种对偶形式.一般力学是基础力学,建立一般力学广义变分原理的对偶形式,对研究变形体力学和力学以外的其他学科的广义变分原理的对偶形式有重要的参考价值.

By using involutory transformations, the stationary conditions of one kind of variables were transformed into basic equations of two kinds of variables. According to corresponding relations between general forces and general displacements, the basic equations were multiplied by corresponding virtual quantities, added algebraically, and then integrated with time. Next, two dual forms of the generalized variational principles of two kinds of variables were established in holonomic systems and nonholonomic systems. Similarly, two dual forms of the generalized variational principles of three kinds of variables were established in holonomic systems and nonholonomic systems. General mechanics is foundational mechanics. It is important to establish dual forms of the generalized variational principles in general mechanics for studying dual forms of the generalized variational principles in deformable body mechanics and other subjects besides mechanics.