Energy-like Liapunov functionals for linear elastic systems on a Hilbert space
Open Access
- 1 January 1973
- journal article
- Published by American Mathematical Society (AMS) in Quarterly of Applied Mathematics
- Vol. 30 (4) , 465-480
- https://doi.org/10.1090/qam/508715
Abstract
An approach is presented for generating energy-like functionals for linear elastic dynamic systems on a Hilbert space. The objective is to obtain a family of functionals which may be used for stability analysis of the equilibrium; i.e., Liapunov functionals. Although the energy functional, when one exists, is always a member of this family, the family is shown to exist even when an energy functional does not. Several discrete and distributed-parameter examples are presented, as are certain specific techniques for utilizing this approach.Keywords
This publication has 10 references indexed in Scilit:
- On the Stability of Some Continuous Systems Subjected to Random ExcitationJournal of Applied Mechanics, 1970
- On the Stability of Linear Discrete Dynamic SystemsJournal of Applied Mechanics, 1970
- Asymptotic behavior of a class of abstract dynamical systemsJournal of Differential Equations, 1970
- Dynamical systems and stabilityJournal of Mathematical Analysis and Applications, 1969
- The effect of damping on the dynamic stability of nonconservative systemsMeccanica, 1968
- Stability theory for ordinary differential equationsJournal of Differential Equations, 1968
- EXTENDED DYNAMICAL SYSTEMS AND STABILITY THEORYProceedings of the National Academy of Sciences, 1967
- Some general considerations concerning the destabilizing effect in nonconservative systemsZeitschrift für angewandte Mathematik und Physik, 1966
- Theory and Application of Liapunov's Direct Method.The American Mathematical Monthly, 1964
- The direct method of Liapunov in stability problems of elastic systemsJournal of Applied Mathematics and Mechanics, 1959