How to neglect specific terms in an expression?

[Robin04]

I've just started using Mathematica and I'm still trying to get used to how things are properly done with it. I tried to do a calculation (this one: https://www.physicsforums.com/threads/lagrangian-of-a-driven-pendulum-landau-problem.965714/) and I had to neglect some terms in an expression.

Is there any tool in Mathematica where I can specify some condition like 'term has explicit time dependence' and it automatically throws out the terms that meet that condition? Or how is this done with these calculations? For now, I just subtracted it from the variable manually but I suppose there's some more elegant way of doing this.

EDIT: As the problem above has been solved I must add that I actually don't need to neglect terms there, because they fall out on their own, but I'm still curious if there are such tools in Mathematica.

 

[Bill Simpson]

Will something like this

Select[a*t*Cos+c*Sin[t]+E^(t-1)+d*Cos+f-1,FreeQ[t]]

which returns this

-1 + f + d*Cos

correctly handle all the cases that you are considering?

You must be very careful with pattern matching methods like this and check that they correctly do exactly what you are expecting in every single case.

Notice for example

Select[a*t*Cos+(c+t)*Sin[g]+E^(t-1)+d*Cos+f-1,FreeQ[t]]

"incorrectly" returns

-1 + f + d*Cos

instead of

-1 + f + d*Cos + c*Sin[g]

if you are expecting this to understand that you intend to eliminate all and only those terms which do not have explicit time dependence.

What is happening, but not shown, is that Plus has a list of arguments, Select is going through that list of arguments at a time, if there is no t in an argument then Select is returning that, otherwise it is discarding that. (c+t)*Sin[g] is one of the arguments in that list. c*Sin[g]+t*Sin[g] is not one of the arguments in that list.

Mathematica does "structural pattern matching", it is simply trying to match the literal structure of expressions, not "semantic pattern matching" or trying to match the meaning of the expression.