Solution
= Solution
For small $\mu$, average $\dot H$ around $x=r\cos2t$, $y=-r\sin2t$. This gives $\langle\dot H\rangle=\mu[r^2-(3a+1)r^4/4]$. The unique positive balance is $r=2/\sqrt{3a+1}$, which lies between $1/\sqrt a$ and $1$ for $a>1$.
= Solution
For small $\mu$, average $\dot H$ around $x=r\cos2t$, $y=-r\sin2t$. This gives $\langle\dot H\rangle=\mu[r^2-(3a+1)r^4/4]$. The unique positive balance is $r=2/\sqrt{3a+1}$, which lies between $1/\sqrt a$ and $1$ for $a>1$.