A Real-Valued Spectral Decomposition of the Undamped Gyroscopic System with Applications
نویسندگان
چکیده
Given an undamped gyroscopic system GðλÞ 1⁄4 Mλ þ CλþK with M , K symmetric and C skew-symmetric, this paper presents a real-valued spectral decomposition of GðλÞ by a real standard pair ðX;TÞ and a skew-symmetric parameter matrix S . When T is assumed to be a block diagonal matrix, the parameter matrix S has a special structure. This spectral decomposition is applied to solve the quadratic inverse eigenvalue problem and the no spill-over quadratic eigenvalue updating problem.
منابع مشابه
Simultaneous Schur decomposition of several nonsymmetric matrices to achieve automatic pairing in multidimensional harmonic retrieval problems
This paper presents a new Jacobi-type method to calculate a simultaneous Schur decomposition (SSD) of several real-valued, nonsymmetric matrices by minimizing an appropriate cost function. Thereby, the SSD reveals the “average eigenstructure” of these nonsymmetric matrices. This enables an R-dimensional extension of Unitary ESPRIT to estimate several undamped R-dimensional modes or frequencies ...
متن کاملAn iterative updating method for damped gyroscopic systems
The problem of updating damped gyroscopic systems using measured modal data can be mathematically formulated as following two problems. Problem I: Given Ma ∈ Rn×n,Λ = diag{λ1, · · · , λp} ∈ Cp×p, X = [x1, · · · , xp] ∈ Cn×p, where p < n and both Λ and X are closed under complex conjugation in the sense that λ2j = λ̄2j−1 ∈ C, x2j = x̄2j−1 ∈ C for j = 1, · · · , l, and λk ∈ R, xk ∈ R for k = 2l+1, ...
متن کاملA new algorithm for solving Van der Pol equation based on piecewise spectral Adomian decomposition method
In this article, a new method is introduced to give approximate solution to Van der Pol equation. The proposed method is based on the combination of two different methods, the spectral Adomian decomposition method (SADM) and piecewise method, called the piecewise Adomian decomposition method (PSADM). The numerical results obtained from the proposed method show that this method is an...
متن کاملSynchrosqueezing-based Transform and its Application in Seismic Data Analysis
Seismic waves are non-stationary due to its propagation through the earth. Time-frequency transforms are suitable tools for analyzing non-stationary seismic signals. Spectral decomposition can reveal the non-stationary characteristics which cannot be easily observed in the time or frequency representation alone. Various types of spectral decomposition methods have been introduced by some resear...
متن کاملSpectral decomposition of real symmetric quadratic λ-matrices and its applications
Spectral decomposition provides a canonical representation of an operator over a vector space in terms of its eigenvalues and eigenfunctions. The canonical form often facilitates discussions which, otherwise, would be complicated and involved. Spectral decomposition is of fundamental importance in many applications. The well-known GLR theory generalizes the classical result of eigendecompositio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Matrix Analysis Applications
دوره 32 شماره
صفحات -
تاریخ انتشار 2011