Orthogonal square root eigenfactor parameterization of mass matrices

作     者：Junkins, JL Schaub, H 

作者机构：Texas A&M University College Station Texas 77843-3141 

出 版 物：《JOURNAL OF GUIDANCE CONTROL AND DYNAMICS》 (J Guid Control Dyn)

年 卷 期：1997年第20卷第6期

页      面：1118-1124页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 08[工学] 0804[工学-仪器科学与技术] 0825[工学-航空宇航科学与技术] 

主　　题：Total Energy Jacobi Method Numerical Integration Numerical Simulation Runge Kutta Methods Parallel Computers Parallel Computing Systems Riccati Equations Taylor Series Computing 

摘      要：An improved method is presented to parameterize a smoothly time varying, symmetric, positive definite system mass matrix M(t) in terms of the instantaneous eigenfactors, namely, the eigenvalues and eigenvectors of M(t), Differential equations are desired whose solutions generate the instantaneous spectral decomposition of M(t). The derivation makes use of the fact that the eigenvector matrix is orthogonal and, thus, evolves analogously to a higher-dimensional rotation matrix. Careful attention is given to cases where some eigenvalues and/or their derivatives are equal or near equal. A robust method is presented to approximate the corresponding eigenvector derivatives in these cases, which ensures that the resulting eigenvectors still diagonalize the instantaneous M(t) matrix, This method is also capable of handling the rare case of discontinuous eigenvectors, which may only occur if both the corresponding eigenvalues and their derivatives are equal.