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| Computation of Gyroscopic System and the Symplectic Eigensolution of Anti-Symmetric Matrix |
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| DOI：10.7511/jslx19933041 |
| KeyWord:gyroscopic system, anti-symmetric matrix, symplectic eigensolution, |
| Zhang Wanxie Lin Jiahao |
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| Abstract: |
| Based on the state vector method, the generalized eigenproblem of linear gyroscopic system, which can be the case of non-positive definite stiffness matrix K,is derived. The weighted adjoint symplectic orthogonality between the eigenvectors and the expansion theorem for an arbitrary state vector are proved. By applying the cell LDLT decomposition for an anti-symmetric matrix, the generalized eigenproblem is reduced to the standard form of a symplectic eigenproblem of an antisymmetric matrix.The symplectic eigenproblem of an anti-symmetric matrix is tranformed to the form of cell semi-tridiagonal matrix by means of the orthogonal SH transformation, and then all its eigensolutions are solved, which gives the foundation of modal analysis for the gyroscopic system. |
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