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:
$V(y_1,y_2)= y_1^2+y_2^2$.
$V(y_1,y_2)= \frac{y_2^2}{2}+(1- \cos(y_1))$.
$V(y_1,y_2)= \frac{(y_1+y_2)^2}{2} + y_1^2 + \frac{y_2^2}{2}$.
Answer
Answers can be viewed only if
- The questioner was satisfied and accepted the answer, or
- The answer was disputed, but the judge evaluated it as 100% correct.
1 Attachment
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to 50% commission on every question your affiliated users ask or answer.
- answered
- 162 views
- $13.00
Related Questions
- Suppose $u \in C^2(\R^n)$ is a harmonic function. Prove that $v=|\nabla u|^2$ is subharmonic, i.e. $-\Delta v \leq 0$
- Equipartition of energy in the wave equation
- Differential equations, question 3
- Solve the initial value problem $(\cos y )y'+(\sin y) t=2t$ with $y(0)=1$
- Differentai equations, question 2.
- Two masses attached to three springs - Differential equations
- Differential equations, question 4
- Ordinary differential equation questions
