- #1
Jamin2112
- 986
- 12
Show that the system has no closed orbits by finding a Lyapunov ...
I'm at the point in the problem where I need constants a and b satisfying
ax2(y-x3) + by2(-x-y3) < 0
and ax2+bx2 > 0
for all (x,y)≠(0,0).
Just in case you're wondering, this is to satisfy the V(x,y)=ax2+by2 > 0 and ΔV(x,y)•<y-x3, -x-y3> < 0 so I can apply that one theorem to my problem.
Well, it seems reasonable to choose a,b>0 to ensure ax2+bx2 > 0, but I'm having trouble figuring out how to make ax2(y-x3) + by2(-x-y3) < 0 simultaneously.
Homework Statement
I'm at the point in the problem where I need constants a and b satisfying
ax2(y-x3) + by2(-x-y3) < 0
and ax2+bx2 > 0
for all (x,y)≠(0,0).
Homework Equations
Just in case you're wondering, this is to satisfy the V(x,y)=ax2+by2 > 0 and ΔV(x,y)•<y-x3, -x-y3> < 0 so I can apply that one theorem to my problem.
The Attempt at a Solution
Well, it seems reasonable to choose a,b>0 to ensure ax2+bx2 > 0, but I'm having trouble figuring out how to make ax2(y-x3) + by2(-x-y3) < 0 simultaneously.