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
3.4K
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
- 567 views
- $13.00
Related Questions
- Differentai equations, question 2.
- Beginner Differential Equations - Growth Rate Question
- 3 Multi-step response questions
- Show that the following subset Ω of Euclidean space is open
- Solving a system of linear ODE with complex eigenvalues
- Find the general solution of the system of ODE $X'=\begin{bmatrix} 1 & 3 \\ -3 & 1 \end{bmatrix} X$
- Laplace transforms and initial value problems.
- Linearization of nonlinear differential equations near an equilibrium position
