= Solution
{c}
With $L=1/\sqrt{n^2-1}$, one has $\nu=n$. Since $n\geq3>\sqrt3$, <4/b/ii> proves boundedness. Write the positive <rational number> $n=p/q$ in lowest terms. The <radius> and its angular <derivative> repeat after $\Delta\theta=2\pi/n$. After $p$ such radial oscillations,
$$
p\Delta\theta=2\pi q,
$$
so both the <position> and the radial and transverse <velocities> return to their initial values. The elapsed time is
$$
T=\frac1L\int_0^{2\pi q}r(\theta)^2\,d\theta,
$$
which is finite and positive because $r$ is bounded above and below by positive constants. Thus \b[the motion is periodic]. The <orbit> is a closed, generally self-intersecting <rosette orbit>, with $p$ radial oscillations during $q$ complete revolutions; for integral $n$ it has $n$ evenly spaced lobes around the origin. It never reaches the origin and is not a <circular orbit>.
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