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Homework Statement
Find whether this system is stable or unstable at the steady state (x1,x2)=(0,0)
dx_{1}/dt = x_{1}+2sin(x_{1})+x_{2}
dx_{2}/dt=2sin(x_{2})
Homework Equations
The Attempt at a Solution
z_{1}=x_{1}0
z_{2}=x_{2}0
dz_{1}/dt=z_{1}+z_{2}+2z_{1}
dz_{2}/dt=2z_{2}
Jacobian =
[ 1 1 ]
[ 0 2 ]
so the system is unstable.
This problem is from my notes from class; I'm not 100% certain that it is written correctly. I am very confused about the part where z_{1} is set equal to x_{1} (I believe this is called linearization)? Could someone please clarify this step for me and how on earth
dx_{2}/dt=2sin(x_{2}) becomes dz_{2}/dt=2z_{2} ?
The rest is pretty straightforward.
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