A linear gyroscopic system is of the form \$\$ M ddot x + Gdot x + K x = 0, \$\$ where the mass matrix \$M\$ is a symmetric positive definite real matrix, the gyroscopic matrix \$G\$ is real and skew-symmetric, and the stiffness matrix \$K\$ is real and symmetric. The system is stable if and only if the quadratic eigenvalue problem \$det(lambda^2 M+lambda G + K)=0\$ has all eigenvalues on the imaginary axis. In this article we are interested in evaluating robustness of a given stable gyroscopic system with respect to perturbations. In order to do this we present an ODE-based methodology which aims to compute the closest unstable gyroscopic system with respect to the Frobenius distance. A few examples illustrate the effectiveness of the methodology.

### Stability of gyroscopic systems with respect to perturbations

#### Abstract

A linear gyroscopic system is of the form \$\$ M ddot x + Gdot x + K x = 0, \$\$ where the mass matrix \$M\$ is a symmetric positive definite real matrix, the gyroscopic matrix \$G\$ is real and skew-symmetric, and the stiffness matrix \$K\$ is real and symmetric. The system is stable if and only if the quadratic eigenvalue problem \$det(lambda^2 M+lambda G + K)=0\$ has all eigenvalues on the imaginary axis. In this article we are interested in evaluating robustness of a given stable gyroscopic system with respect to perturbations. In order to do this we present an ODE-based methodology which aims to compute the closest unstable gyroscopic system with respect to the Frobenius distance. A few examples illustrate the effectiveness of the methodology.
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2019
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11697/145780`
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