变质量挠性体动力学普遍方程(二)

Universal dynamic equations for flexiable body with variable mass:Ⅱ

将固体燃料运载火箭视为时变边界的挠性体能更精确地刻划其动力学行为 :燃料的喷射伴随着质量和边界的变化 ,而边界的时变特性决定了火箭的质心位置和转动惯量张量时变特性及轨道与姿态运动强耦合作用 .将挠性体与其外部的质量交换当做作用于时变边界上的表面力 ,采用连续介质力学中的平衡理论和分析力学中的变分原理对时变边界挠性体的动力学行为进行研究 ,建立了这类挠性体的动力学方程 .将时变边界刚体作为时变边界挠性体的特例 ,列出了它的动量平衡律和动量矩平衡律 ,并得出如下结论 :一般情况下挠性体的时变边界是难以确定的 ,因此必须对挠性体的时变边界作出某些简化才能得到其动力学问题的解 .

The dynamical behavior of a solid fuel rocket can be described more accurately if the rocket can be taken as a flexible body with variable boundary .The jet of solid fuel out from a rocket is accompanied by the variation of mass and boundary of the rocket, and further more , by the change of location of mass center and the inertial tensor of rotation with respect to the coordinate system rooted on the rocket itself. On this account, strong coupling between the trajectory movement and attitude movement exists. A superficial study is done on the dynamical behavior of flexible body with variable boundary by applying the conservation laws in continual mechanics and variational principle in analytical mechanics, and the dynamic equations of this kind of flexible body is established. The action of mass exchange between the flexible body and the exterior is considered as surface force acting on the variable boundary,and the corresponding boundary condition is defined. As an especial condition, a rigid body with variable boundary is considered. It is pointed that that the variable boundary can hardly be determined in general variable mass system, and some preconditions should be imposed to work out the dynamical problem of flexible body with variable boundary.