Orchestration books warn composers about trombone music which requires excessive movements of the slide.

How serious is this problem? How should a composer, who does not play the trombone, handle it?

The best way? Have an experienced trombone player take a quick look at it. Only takes a moment, and we can tell you pretty much immediately if it is doable or not.

If you need, you can even post here and we can give you tips and pointers. Eventually, you will get the gist of it.

My first suggestion is read your reference books and see if there are any suggestions there.

2nd suggestions - look at sucessful composers trombone parts, see how they are using the trombone.

3rd suggestion - write something and then take it to a good trombone player and have them play it and critique it for you. Tell them what you are trying to do and they will give you a proper critique. If you don't tell them they might be too nice and not tell you about somewhat hard things.

4th suggestion. Stipulate in your music that the parts should only be played on trombones with a G trigger assembly.

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The 4th suggestion would work, but is really intended for a litte bit of humor.

For the most part, you're only going to have to worry about excessive slide motion in the lower register, and those with F attachments have less problems. But really, it's not your problem, it's the player's.
Honestly, (and I may be the opposing view here), don't worry so much about it. Write what you hear in your head, and write what supports your musical idea. Leave it up to the player to figure out how to play it, unless you are specifically writing for school level players.

Thank you, all, very much. My thanks are especially to Steve, for providing me with the worth while information that excessive slide motion may become problematic only in the lower register. Now, where is the dividing line between the lower register and the upper registers for the bass trombone and for the tenor trombone (and what about the alt trombone? According to the orchestration books it is not in use any more, but what I hear from you, trombone players, does not necessarily agree with the books. Is there any point in considering the alt trombone?)

Up until now I did not dare to write for the trombone. I have decided to give it a try. I have an idea to work on. If it develops into a satisfactory piece, I will be happy to post it here, hoping that you will like it and enjoy playing it.

Thanks again