現代物理学の非保存安定性問題 Non-conservative Stability Problems of Modern Physics (De Gruyter Studies in Mathematical Physics 14) （2013. XVII, 429 S. 109 b/w ill., 4 b/w tbl. 240 mm）

現代物理学の非保存安定性問題<br>Non-conservative Stability Problems of Modern Physics (De Gruyter Studies in Mathematical Physics 14) （2013. XVII, 429 S. 109 b/w ill., 4 b/w tbl. 240 mm）

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現代物理学の非保存安定性問題
Non-conservative Stability Problems of Modern Physics (De Gruyter Studies in Mathematical Physics 14) （2013. XVII, 429 S. 109 b/w ill., 4 b/w tbl. 240 mm）

Kirillov, Oleg N.

ウェブストア価格 ¥37,095（本体¥33,723）
DE GRUYTER（2013発売）
外貨定価 EUR 149.95
ポイント 337pt

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製本 Hardcover:ハードカバー版／ページ数 440 p.
商品コード 9783110270341

基本説明

This book combines modern applied mathematics with the complex fundamental non-conservative phenomena of physics and mechanics.

Full Description

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.

Introduction. Historical overviewChapter 1. Lyapunov stability and linear stability analysisChapter 2. Sources of linear equations with parametersChapter 3. Typical classes of systems: Hamiltonian systemsChapter 4. Typical classes of systems: reversible systemsChapter 5. Characteristic polynomial and dispersion relationChapter 6. Influence of structure of forces on stabilityChapter 7. The Ziegler-Bottema paradox in near-reversible systemsChapter 8. Near-Hamiltonian systemsChapter 9. Non-self-adjoint boundary eigenvalue problems for differential operators and operator matrices dependent on parametersChapter 10. Destabilization paradox in distributed circulatory systemsChapter 11. MHD mean field alpha-2 dynamoChapter 12. Campbell diagrams and wave propagation in rotating continuaChapter 13. Non-Hermitian perturbations of Hermitian operators and crystal opticsChapter 14. Magnetorotational instabilityChapter 15. Non-conservative systems with kinematics constraintsConclusionReferences