Chetaev instability theorem
- 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 V and both are of the same sign does not have to be produced.
It is named after Nicolai Gurevich Chetaev.
- Lyapunov function — a function whose existence guarantees stability
- Rumyantsev, V. V. (2001) , "Chetaev theorems", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4