The Chetaev instability theorem for

dynamical system In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water i ...

s states that if there exists, for the system

\dot = X(\textbf)

with an

equilibrium point In mathematics, specifically in differential equations, an equilibrium point is a constant solution to a differential equation. Formal definition The point \tilde\in \mathbb^n is an equilibrium point for the differential equation :\frac = \m ...

at the origin, a continuously differentiable function V(x) such that # the origin is a boundary point of the set

G = \

; # there exists a neighborhood

U

of the origin such that

\dot(\textbf)>0

for all

\mathbf \in G \cap U

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

\dot

both are of the same sign does not have to be produced. It is named after Nicolai Gurevich Chetaev.

Applications

Chetaev instability theorem has been used to analyze the unfolding dynamics of proteins under the effect of optical tweezers.

Applications

See also

References

Further reading