充液航天器自旋稳定性分析的一种近似方法

研究充液航天器在液体晃动、航天器平动和摆动相互耦合情况下的自旋稳定性问题 .采用Galerkin方法建立液体受迫振动的离散动力学方程 ,并对液体自由振动的特征问题建立了有限元数值计算方法 .由系统的动量方程、动量矩方程和液体受迫振动方程建立刚 -液耦合系统的姿态动力学方程 ,并由 Kelvin定理给出了充液航天器的自旋稳定性判据 .通过有限元分析 ,消去稳定性判据中的液体晃动特征模态矩阵 ,从而得到稳定性判据与充液腔体无关而仅与液体自由面有关的结论 .稳定性判据适用于带任意形状的轴对称充液腔的自旋航天器系统 .

An Approximate Solution to the Spinning Stability Criterion of Spacecraft Partially Filled with Liquid

The spinning stability of a spacecraft partially filled with inviscid,incompressible liquid was in- vestigated.The coupled effect of liquid sloshing,translation and nutation of the spacecraft was consid- ered.Numerical treatment of the characteristic problem of the free vibration of liquid in a spinning contain- er was established,which depends on the establishment of the extreme- value principle of a functional de- rived from the boundary- value problem.The forced motion of liquid due to translation and nutation of the spacecraft was expressed in Ritz form and then employing Galerkin's method the closed- form set of the at- titude dynamic equation of the system was obtained.Using Kelvin's theorem,the stability criterion was given.Further investigation shows that the eigenmodal matrix of sloshing can be eliminated in the expres- sion of stability criterion,which yields an approximate method simplifying the criterion.Thus it comes to a conclusion that the stability criterion is suitable to arbitrary axisymmetric tank.Numerical results were given which show good agreement to the analytical ones.