The Chetaev instability theorem for dynamical systems states that if there exists, for the system with an equilibrium point at the origin, a continuously differentiable function V(x) such that
- the origin is a boundary point of the set ;
- there exists a neighborhood of the origin such that for all
then the origin is an unstable equilibrium point of the system.
This theorem is somewhat less restrictive than the Lyapunov instability theorems, since a complete sphere (circle) around the origin for which and both are of the same sign does not have to be produced.
It is named after Nicolai Gurevich Chetaev.
Applications
editChetaev instability theorem has been used to analyze the unfolding dynamics of proteins under the effect of optical tweezers.[1]
See also
edit- Lyapunov function — a function whose existence guarantees stability
References
edit- ^ Mohammadi, A.; Spong, Mark W. (2022). "Chetaev Instability Framework for Kinetostatic Compliance-Based Protein Unfolding". IEEE Control Systems Letters. 6: 2755–2760. arXiv:2205.07375. doi:10.1109/LCSYS.2022.3176433. ISSN 2475-1456.
- Rumyantsev, V. V. (2001) [1994]. "Chetaev theorems". Encyclopedia of Mathematics. EMS Press.
Further reading
edit- Shnol, Emmanuil (2007). "Chetaev function". Scholarpedia. 2 (9): 4672. Bibcode:2007SchpJ...2.4672S. doi:10.4249/scholarpedia.4672.