We know that there is a function VariationalMethods`EulerEquations
readily handling the Euler-Lagrange equation of the "standard" form
$$ \frac{\partial L}{\partial q} - \frac{\mathrm d}{\mathrm d t}\left(\frac{\partial L}{\partial \dot q}\right) = 0. $$
But today, it suddenly occurs to me that problems [e.g., see Eqs. (5) & (6) in this note] with a damping term are not included, are they?
My question is, is there any hidden magic in VariationalMethods`EulerEquations
that makes it still capable of dealing with equations like
$$ \frac{\partial L}{\partial q} - \frac{\mathrm d}{\mathrm d t}\left(\frac{\partial L}{\partial \dot q}\right) - \frac{\partial F}{\partial \dot q} = 0, \qquad F = \frac{b}{2}\dot q^2, $$
or one has to return to manual establishment of equations of motion using functions like D
or VariationalMethods`VariationalD
?
0
on the RHS with the generalized force? $\endgroup$