= Routhian
{c}
{title2=$R=L-\sum_i p_i\dot q_i$}
Use the convention $R=L-\sum_i p_i\dot q_i$ for the eliminated <cyclic coordinates>, expressing their velocities in terms of their fixed <conjugate momenta>. Terms involving derivatives of those eliminated velocities cancel because $\partial L/\partial\dot q_i=p_i$. Thus the remaining coordinates obey the usual <Euler-Lagrange equations> for R. For a particle of fixed <angular momentum> $\ell$ in a central potential, this gives $R=m\dot r^2/2-V(r)-\ell^2/(2mr^2)$, rather than the expression obtained by direct substitution into L alone. An opposite overall sign convention is also used, with correspondingly signed mixed Hamiltonian equations.
Back to article page
