Explicitly dependent on time Lagrangian

[Magister]

I need to turn this Lagrangian in one that is not explicitly dependent on time.

$$L = \frac{\alpha}{2} (q^\prime + qbe^{-\alpha t})^2-q^2 \frac{ab}{2} e^{-\alpha t} (\alpha +b e^{-\alpha t})- \frac{k q^2}{2}<br />$$

I have already spent a lot of time around this problem but I am far from getting a satisfactory answer. Is there any method for doing this or is just by looking? Any help would be great! Thanks

 

[Mentz114]

Is there a transformation $$q ->\bar{q }= qf(\alpha + be^{-\alpha t})$$ that puts the explicit time dependence into q ?