应用 Lagrange方程研究刚弹耦合动力学

摘要

How to apply Lagrange equation in continuum mechanics is a hot theoretical topic in the academic field. The establishment and application of Lagrange equation is related to variational calculus.It is a suitable way to stud-y such questions by the basic theory of variational calculus.Applying the concept and algorithm of a variational de-rivative, the properties of derivation in Lagrange equation are studied.Further Lagrange equation is applied to elas-to-dynamics successfully.According to the work and energy principle and the energy conservation law, the kinetic and potential energies of rigid-elastic coupling dynamics are obtained.The governing equations of rigid-elastic cou-pling dynamics are established using Lagrange equation.This kind of research has important application in the aero-space, aviation, navigation and robot dynamics fields.%如何将Lagrange方程应用于连续介质力学，一直是学术界关注的理论课题。 Lagrange方程建立和应用都涉及变分学，从变分学的基本理论研究做起，是研究这类问题的一条可行的途径。应用变导的概念和运算法则，研究了La-grange方程中的求导的性质，进而成功地将Lagrange方程应用于弹性动力学。根据功能原理和能量守恒定律，给出刚弹耦合动力学的动能和势能，应用Lagrange方程，建立了刚弹耦合动力学的控制方程。这类研究在航天、航空、航海和机器人动力学中，都有重要应用。