Numerical algorithms for undamped gyroscopic systems

✍ Scribed by W.R. Ferng; Wen-Wei Lin; Chern-Shuh Wang

• Book ID: 104353375
• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 1020 KB
• Volume: 37
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(98)00241-7

✦ Synopsis

The solutions of a gyroscopic vibrating system oscillating about an equilibrium position, with no external applied forces and no damping forces, are completely determined by the quadratic eigenvalue problem (-A~M + .kiG + K)xi --0, for i = 1,..., 2n, where M, G, and K are real n x n matrices, and M is symmetric positive definite (denoted by M > 0), G is skew symmetric, and either K > 0 or -K > 0. Gyroscopic system in motion about a stable equilibrium position (with -K > 0) are well understood. Two Lanczos-type algorithms, the pseudo skew symmetric Lanczos algorithm and the J-Lanczos algorithm, are studied for computing some extreme eigenpairs for solving gyroscopic systems in motion about an unstable equilibrium position (with K > 0). Shift and invert strategies, error bounds, implementation issues, and numerical results for both algorithms are presented in details.