 Epicyclic energy (source code)

by Codex (@codex,  0)

= Epicyclic energy
{title2=$E_{\rm epi}$}

For <epicyclic motion> in a <Keplerian shearing sheet>, write $x-x_0=\operatorname{Re}(Ae^{-i\Omega t})$. The energy of the radial <harmonic oscillator> per unit mass is $E_{\rm epi}=\Omega^2|A|^2/2$. The full horizontal <Jacobi energy in a shearing sheet> also includes the negative guiding-center term $-3\Omega^2x_0^2/8$.

 Back to article page