# Lyapuniv-functions

We have the system of ODEs

$y_1'= y_2$

$y_2'=-y_2-\sin(y_1)$.

Decide for each of the following functions whether it is a Lyapunov-function of $(0,0)$ or not:

$V(y_1,y_2)= y_1^2+y_2^2$.

$V(y_1,y_2)= \frac{y_2^2}{2}+(1- \cos(y_1))$.

$V(y_1,y_2)= \frac{(y_1+y_2)^2}{2} + y_1^2 + \frac{y_2^2}{2}$.

Ichbinanonym

101

## Answer

**Answers can only be viewed under the following conditions:**

- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.

1 Attachment

Mathe

3.2K

The answer is accepted.

Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.

- answered
- 413 views
- $13.00

### Related Questions

- Laplace transforms / ODE / process model
- Differential Equations
- Solve the two-way wave equation in terms of $u_0$
- A linear ODE
- Diffrential Equations
- Show this initial value problem has a unique solution for initial value forall t
- How should I approach this question?
- Find the general solution of the system of ODE $X'=\begin{bmatrix} 1 & 3 \\ -3 & 1 \end{bmatrix} X$