A Study for Quadratic Eigenvalue Problems of Gyroscopic Systems

• Main Authors: Chih-Chiang Yang, 楊智強
• Other Authors: Yuen-Cheng Kuo
• Format: Others
• Language: en_US
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/59kp4g

碩士 === 國立高雄大學 === 應用數學系碩士班 === 96 === We are interested in the quadratic eigenvalue problem (QEP) of gyroscopic systems G(λ )x ≡ (λ2M + λG + K)x = 0 , where M = M Τ , , . Among current developments, the quadratic inverse eigenvalue problem (QIEP) is particularly more important and challenging. In this paper, we mainly consider a general solution for a QIEP of gyroscopic system with prescribed eigenpairs . Let G = −GΤ K = K Τ �k ℜn×n m := n + k m i i i x 1 {( , )} = λ k := 1+ 1+ n * . If , we can construct that, generically, there is a nonsingular quadratic pencil * 0 ≤ k ≤ k G(λ ) such that ( ) = 0 i i G λ x , for i = 1,L,m . Otherwise, if k ≤ k ≤ n * , we show that, generically, all quadratic pencil solutions are singular. We also derive the dimension of the solution subspace of the QIEP for both cases. Furthermore, we utilize some results to display an application of QIEP. Finally, the results of numerical examples illustrate our main consequences.