The Lyapunov-Movchan method in problems of the stability of flows and deformation processes. (English. Russian original) Zbl 1432.74086
J. Appl. Math. Mech. 78, No. 6, 621-633 (2014); translation from Prikl. Mat. Mekh. 78, No. 6, 862-885 (2014).
Summary: 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.
MSC:
| 74H55 | Stability of dynamical problems in solid mechanics |
| 37B25 | Stability of topological dynamical systems |
| 37C75 | Stability theory for smooth dynamical systems |
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