一种不含待定乘子的理想约束系统的动力学建模

A type of dynamical equations for systems subjected to ideal constraints without unknown multipliers

为了克服应用罗斯方法所建立的理想约束系统的动力学方程中含有待定乘子以及方程的数目和未知变量的个数都比较多的这种缺陷,本文从广义坐标形式的动力学普遍方程出发,并结合系统的约束方程,推导出一种不含待定乘子的理想约束系统的动力学方程组,并给出了应用该方程组完成理想约束系统动力学建模的具体步骤。本文所建立的理想约束系统的动力学方程组相对于应用罗斯方法所建立的动力学方程组,具有不含待定乘子且方程和未知变量的个数都比较少的优点。文中通过两个动力学建模的实例证实了上述优点。

In order to overcome the deflects of dynamical equations for systems subjected to ideal constraints established using Routh method, a type of dynamical equations for the systems without unknown multipliers are derived from general equations of dynamics in terms of generalized coordinates and constraint equations. A method of dynamical modeling for systems subjected to ideal constraints is given. Compared with the dynamical equations established using Routh method, the equations presented in this paper possess the advantages of fewer unknown variables, fewer equations and no unknown multipliers. Two examples of dynamic modeling demonstrate the above advantages.