中文摘要：

文中在精确描述柔性梁非线性变形的基础上，利用有限元方法对梁结构进行离散，然后针对具有大范围运动的平面柔性梁结构利用Lagrange方程建立系统的精确动力学方程。该方程在原有一次耦合模型的基础上，增加了新的表征纵向、横向、侧向弯曲变形，以及扭转变形的耦合项。所得方程可用于研究非惯性系下的结构动力学问题，也可用于大范围运动为未知的刚柔耦舍问题。

英文摘要：

Aim. In astronautical applications, particularly in spacecraft, the dynamic modeling of a flexible beam is essential; yet existing such models, in our opinion, lack several important coupling terms. We now supply these important coupling terms. In the full paper, we explain our better model in some detail. In this abstract, we just add some pertinent remarks to listing the two topics of explanation. The first topic is： the kinematic analysis of a flexible beam with large overall motion. The second topic is： the dynamic equations of a flexible beam with large overall motion. Its four subtopics are： the kinetic energy of the flexible beam（subtopic 2.1）, the potential energy of the flexible beam（subtopic 2.2）, generalized force corresponding to external force （subtopic 2.3）, and dynamic equations for a rigid-flexible coupling beam（subtopic 2.4）. The last sentence of subtopic 2.1 describes clearly what are the important coupling terms added in our better model using finite element method. In subtopic 2.2,using the non-linearity of displacement and strain of the flexible beam, we obtain its potential energy. In subtopic2.3, we obtain the generalized force corresponding to external force as shown in eq. （23） in the full paper. In subtopic 2. 4, using the Lagrange＇s equations, we derive the dynamic equation（eq. 24 in the full paper） for a rigid-flexible beam without knowledge of its motion laws.