- #1
rmiller70015
- 110
- 1
Homework Statement
For the system:
[tex]
\frac{dx}{dt}=x\cos{xy}
\: \:
\frac{dy}{dt}=-y\cos{xy}[/tex]
(a) is Hamiltonian with the function:
[tex]
H(x,y)=\sin{xy}[/tex]
(b) Sketch the level sets of H, and
(c) sketch the phase portrait of the system. Include a description of all equilibrium points and any saddle connections.
Homework Equations
The Attempt at a Solution
[tex]\frac{\partial H}{\partial y}=y\cos{xy}=-g \\
\frac{\partial H}{\partial x}=x\cos{xy}=f[/tex]
So the function is Hamiltonian. I see that the equilibrium points are (0,0) and (±√π/2,±√π/2) by inspection. The problem I have is that the second set of equilibria have complex roots, but I don't see any of that behavior when I graph the phase portrait with pplane.