刚-液耦合航天器系统的Hamilton结构及稳定性分析  

Hamiltonian Structures and Stability Analysis for Rigid⁃Liquid Coupled Spacecraft Systems

作　　者：易中贵 岳宝增[2] 刘峰 卢涛 邓明乐 YI Zhonggui;YUE Baozeng;LIU Feng;LU Tao;DENG Mingle(School of Mathematics and Statistics,Beijing Institute of Technology,Beijing 100081,P.R.China;School of Aerospace Engineering,Beijing Institute of Technology,Beijing 100081,P.R.China;Beijing Institute of Astronautical Systems Engineering,Beijing 100076,P.R.China;Institute of Telecommunication and Navigation Satellites,China Academy of Space Technology,Beijing 100094,P.R.China)

机构地区：[1]北京理工大学数学与统计学院,北京100081 [2]北京理工大学宇航学院,北京100081 [3]北京宇航系统工程研究所,北京100076 [4]中国空间技术研究院通信与导航卫星总体部,北京100094

出　　处：《应用数学和力学》2023年第5期499-512,共14页Applied Mathematics and Mechanics

基　　金：国家国防科技工业局民用航天“十三五”技术预先研究项目(D020201);国家自然科学基金(重点项目)(12132002);国家自然科学基金(面上项目)(11772049);国家自然科学基金青年科学基金项目(12202044)。

摘　　要：该文采用3D刚体摆来等效推进剂的非线性晃动行为.由此研究了该刚-液耦合航天器系统的Hamilton结构,介绍了系统的R^(3)约化(对应系统的平移不变性或总线动量不变性)以及S_(o)(3)约化(对应系统的旋转不变性或总角动量不变性),并推导了系统在约化空间s^(∗)_(o)(3)×s^(∗)_(o)(3)×S_(o)(3)上的约化Poisson括号.接着研究了刚-液耦合航天器系统的自旋稳定性特征,先根据对称临界原理推导了刚-液耦合航天器系统的相对平衡态,由此根据能量-动量方法与分块对角化技术,推导了系统的自旋稳定性条件和Arnold形式的稳定性边界.最后根据具体模型参数,给出了以图形方式展现的自旋稳定域.For the dynamics problems of rigid⁃liquid coupling spacecraft systems with liquid propellant,a 3D rigid pendulum model was used to simulate the nonlinear sloshing behavior of the propellant.On this basis,the Hamiltonian structure of the rigid⁃liquid coupling spacecraft system was studied,the R^(3) reduction(correspond⁃ing to the translation invariance or the bus momentum invariance of the system)and the S_(o)(3)reduction(cor⁃responding to the rotation invariance or the total angular momentum invariance of the system)of the system were introduced,with the reduced Poisson brackets of the system in reduced space s^(∗)_(o)(3)×s^(∗)_(o)(3)×S_(o)(3)de⁃rived.Then,the spin stability characteristics of the rigid⁃liquid coupled spacecraft system were studied.Firstly,the relative equilibrium of the rigid⁃liquid coupled spacecraft system was derived under the principle of symmet⁃ric criticality.Based on the energy⁃momentum method and the block diagonalization technology,the spin stabil⁃ity conditions and the Arnold form stability boundaries of the system were derived.Finally,the spin stability do⁃mains illustrated in the form of graph were given according to the specific model parameters.

关 键 词：液体非线性晃动 等效力学模型 HAMILTON结构 稳定性分析 能量-动量方法 

分 类 号：O302[理学—力学]