Nonconservative stability problems of modern physics
- by Oleg N. Kirillov.
- Berlin ; Boston : Walter de Gruyter GmbH & Co., KG, 
- Copyright notice
- Physical description
- 1 online resource (xvii, 429 pages) : illustrations.
- De Gruyter studies in mathematical physics ; 14.
- Kirillov, Oleg N., 1972- author.
- Includes bibliographies (pages -422) and indexes.
- Introduction. Historical overview
- Chapter 1. Lyapunov stability and linear stability analysis
- Chapter 2. Sources of linear equations with parameters
- Chapter 3. Typical classes of systems: Hamiltonian systems
- Chapter 4. Typical classes of systems: reversible systems
- Chapter 5. Characteristic polynomial and dispersion relation
- Chapter 6. Influence of structure of forces on stability
- Chapter 7. The Ziegler-Bottema paradox in near-reversible systems
- Chapter 8. Near-Hamiltonian systems
- Chapter 9. Non-self-adjoint boundary eigenvalue problems for differential operators and operator matrices dependent on parameters
- Chapter 10. Destabilization paradox in distributed circulatory systems
- Chapter 11. MHD mean field alpha-2 dynamo
- Chapter 12. Campbell diagrams and wave propagation in rotating continua
- Chapter 13. Non-Hermitian perturbations of Hermitian operators and crystal optics
- Chapter 14. Magnetorotational instability
- Chapter 15. Non-conservative systems with kinematics constraints Conclusion References.
- (source: Nielsen Book Data)
This work gives a complete overview on the subject of nonconservative stability from the modern point of view. Relevant mathematical concepts are presented, as well as rigorous stability results and numerous classical and contemporary examples from mechanics and physics. It deals with both finite- and infinite-dimensional nonconservative systems and covers the fundamentals of the theory, including such topics as Lyapunov stability and linear stability analysis, Hamiltonian and gyroscopic systems, reversible and circulatory systems, influence of structure of forces on stability, and dissipation-induced instabilities, as well as concrete physical problems, including perturbative techniques for nonself-adjoint boundary eigenvalue problems, theory of the destabilization paradox due to small damping in continuous circulatory systems, Krein-space related perturbation theory for the MHD kinematic mean field (2)-dynamo, analysis of Campbell diagrams and friction-induced flutter in gyroscopic continua, non-Hermitian perturbation of Hermitian matrices with applications to optics, and magnetorotational instability and the Velikhov-Chandrasekhar paradox. The book serves present and prospective specialists providing the current state of knowledge in the actively developing field of nonconservative stability theory. Its understanding is vital for many areas of technology, ranging from such traditional ones as rotor dynamics, aeroelasticity and structural mechanics to modern problems of hydro- and magnetohydrodynamics and celestial mechanics.
(source: Nielsen Book Data)
- Publication date
- Copyright date
- De Gruyter Studies in Mathematical Physics ; 14
- 3.3.7 Inertia theorems and stability of gyroscopic systems.
- 9783110270433 (electronic bk.)
- 3110270439 (electronic bk.)