Reversible dynamical systems: Dissipation-induced destabilization and follower forces. (English) Zbl 0822.93038
Summary: This paper uses results from the theory of reversible dynamical systems to examine the nonlinear stability of undamped follower force systems. The dissipation-induced destabilization found in these systems is also examined and it is indicated how the postdestabilization dynamics can be determined using normal forms and an eigenvalue splitting criterion.
MSC:
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 37G05 | Normal forms for dynamical systems |
| 93B60 | Eigenvalue problems |
Keywords:
reversible dynamical systems; stability; dissipation; destabilization; normal forms; eigenvalueReferences:
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