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This work provides a comprehensive overview of nonconservative stability from a modern perspective. It presents relevant mathematical concepts, rigorous stability results, and numerous examples from mechanics and physics. The focus is on both finite- and infinite-dimensional nonconservative systems, covering fundamental theories such as Lyapunov stability, linear stability analysis, Hamiltonian and gyroscopic systems, and the effects of force structure on stability. Key topics include dissipation-induced instabilities and specific physical problems like perturbative techniques for nonself-adjoint boundary eigenvalue issues, the destabilization paradox due to small damping in continuous circulatory systems, and Krein-space related perturbation theory for the MHD kinematic mean field α²-dynamo. Additionally, it analyzes Campbell diagrams, friction-induced flutter in gyroscopic continua, non-Hermitian perturbations of Hermitian matrices in optics, and magnetorotational instability alongside the Velikhov-Chandrasekhar paradox. This book is essential for current and prospective specialists, offering insights into the evolving field of nonconservative stability theory, which is crucial for various technological applications, including rotor dynamics, aeroelasticity, structural mechanics, and modern challenges in hydro- and magnetohydrodynamics and celestial mechanics.
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Nonconservative stability problems of modern physics, Oleg N. Kirillov
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- Pubblicato
- 2013
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