How to drop terms in a Lagrangian?

Hi guys,

So textbooks have it that: "Two Lagrangians differing by a total time-derivative of a function of the coordinates are equivalent". I have no idea what that means or how to use it; so I dont know which terms I can drop from Lagrangians, which is a bit of a problem.

For example, consider a random example... a simple pendulum of length [itex]l[/itex] and mass [itex]m[/itex]. I'll spice it up a bit by saying that the point of suspension can move vertically according to the law [itex]y = la(t)[/itex], where obviously [itex]a[/itex] is a function of time.

If you consider the angle between the pendulum and the vertical, [itex]θ[/itex], to be the degree of freedom, you end up with the Lagrangian:

[itex]L = T - V = \frac{1}{2}ml^{2}[\dot{a}(t) - 2sin(θ)\dot{a}(t)\dot{θ}+\dot{θ}^{2}] - mgl[a(t) + cos(θ)] [/itex]

Could you please explain what that "differing by a total time-derivative of a function of the coordinates..." thing means by demonstrating on this example Lagrangian which terms I can drop? or any other way you think is best? You dont HAVE to demonstrate on this particular example, I just thought it might help if you had a Lagrangian to play with.

Thanks a lot!