d dPR dPR d dPR dPR
-- ----- - ----- = Q1, -- ----- - ---- = Q2, ... (8)
dt dPq`1 dPq1 dt dPq`2 dPq2
These are Routh's forms of the modified Lagrangian equations.
Equivalent forms were obtained independently by Helmholtz at a later
date.
Kelvin's equations.