论文部分内容阅读
本文使用旋量与图论概念相结合的方法建立弹性联系的树形多刚体系统的普遍动力学方程。此方程也适用于讨论构件之间无刚体位移的弹性结构物的运动。采用旋量的矩阵记法使全部计算过程具有统一的矩阵形式及程式化步骤。以带偏心飞论及太阳翼的弹性结构卫星作为具体算例。弹性联系的多刚体系统是带挠性附件的航天器或考虑弹性变形的机构、机械手及其它工程对象的动力学模型。系统内的主要构件仍作为刚体,结构弹性只由联接铰的弹性变形所体现。近代航天器常带有许多可动部件,考虑联接铰的弹性变形后,系统的自由度变得十分庞大,按传统的拉格朗日方建立动力学方程,其计算过程适于繁琐而难以采用。除以一般多刚体系统为对象的Kane方法及Roberson—Wittenburg方法以外,本文提出将旋量与图论概念相结合的方法应用于弹性联系的树形多刚体系统,建立其普遍动力学方程。以带偏心飞轮及太阳翼的弹性结构卫星作为具体算例,并与Kane方法进行比较。
In this paper, we establish a general dynamic equation of a tree-shaped multi-rigid-body system with elastic relations by means of a combination of spin and graph theory. This equation is also suitable for discussing the movement of elastic structures without rigid body displacement between the components. The use of spin-spin matrix notation makes the entire calculation process has a uniform matrix and stylized steps. Taking the elastic structure satellite with eccentricity theory and solar wing as a concrete example. The multi-rigid system that is elastically linked is a dynamic model of a spacecraft with flexible attachments or a mechanism that considers elastic deformation, a manipulator, and other engineering objects. The main components of the system are still rigid body, the structural flexibility is only reflected by the elastic deformation of the joint hinge. Modern spacecraft often with many moving parts, considering the elastic deformation of the joint hinge, the system becomes very large degree of freedom, according to the traditional Lagrange set up kinetic equations, the calculation process is cumbersome and difficult to adopt . In addition to the Kane method and the Roberson-Wittenburg method, which are general multi-rigid-body systems, this paper proposes a method of combining the spin and the concept of graph theory in a tree-shaped multi-rigid system with elastic relations and establishes its general dynamic equation. The elastic structure satellite with eccentric flywheel and solar wing is taken as a specific example and compared with Kane method.