Speaker
Description
In this talk, we will consider a linear gyroscopic mechanical systems of the form
\begin{equation}\displaystyle M \ddot x(t) + G\dot x(t) + K x(t) = 0,
\end{equation}
where the mass matrix $M\in\mathbb{R}^{n\times n}$ and the stiffness matrix $K\in\mathbb{R}^{n\times n}$ are symmetric positive definite matrices, while the gyroscopic matrix $G \in\mathbb{R}^{n\times n}$ is skew-symmetric, i.e., $G^T=-G$, and $x=x(t)$ is a time-dependent displacement vector.
The properties of the system are defined by those of the associated quadratic eigenvalue problem (QEP)\begin{equation}
{\mathcal G}(\lambda)x=(\lambda^2M+\lambda G+K)x=0, \quad 0\neq x\in\mathbb{C}^{n}.
\end{equation} We will provide an overview of various linearizations and transformations of the QEP that can be used to develop efficient numerical methods for applications such as stability analysis of gyroscopic systems or perturbation theory.
