Epicyclic guiding center
= Epicyclic guiding center
{title2=$x_0$}
The epicyclic guiding center is the circular-orbit location about which a particle performs <epicyclic motion>. In a <Keplerian shearing sheet>, the conserved <canonical momentum> is $p_y=\dot y+2\Omega x=\Omega x_0/2$. The guiding center therefore labels the particle's first-order <specific angular momentum> offset, even while its instantaneous radial coordinate oscillates.