The Lyapunov–Movchan method in problems of the stability of flows and deformation processes
The extension of Lyapunov's method to continuous mechanical systems are discussed. An annotated bibliography of papers is given in which, based on the Lyapunov–Movchan method, with the construction of corresponding functionals, a direct analysis is carried out of the stability of motion (deform...
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| Veröffentlicht in: | Journal of applied mathematics and mechanics 2014-01, Vol.78 (6), p.621-633 |
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| container_title | Journal of applied mathematics and mechanics |
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| creator | Georgievskii, D.V. Kvachev, K.V. |
| description | The extension of Lyapunov's method to continuous mechanical systems are discussed. An annotated bibliography of papers is given in which, based on the Lyapunov–Movchan method, with the construction of corresponding functionals, a direct analysis is carried out of the stability of motion (deformation) of continuous mechanical systems. The material is divided into sections, devoted to the following: (a) the extension of the mathematical apparatus as a whole to continuous and dynamic systems, (b) the stability of elastic, elastoplastic and viscoelastic deformable solids, (c) stability in aeroelasticity and hydroelasticity theory, (d) the linearized theory of hydrodynamic stability, and (e) the stability with reference to perturbations of material functions in the theory of constitutive relations. |
| doi_str_mv | 10.1016/j.jappmathmech.2015.04.010 |
| format | Article |
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| subjects | Constitutive relationships Deformation Dynamical systems Dynamics Elastoplasticity Mathematical analysis Mechanical systems Stability |
| title | The Lyapunov–Movchan method in problems of the stability of flows and deformation processes |
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