Practicing while tired.
Does it do any good to practice when you just want to sleep? After a long day at work or school, is it worth it to stay up a few more hours to get practice in?
The first thing to practice is... To practice.
A remedy that works for me: a 15-minute power-nap in late afternoon to get recharged for an upcoming practice session. I avoid caffeine and stimulants. When you're tired, these props don't solve the problem but just put the mind and body to cross-purposes.
Physical tiredness is less of an issue than mental tiredness. As long as you've got normal fatigue, as opposed to fatigue caused by, say, a strenuous manual-labor job or hours of athletic practice -- you won't injure yourself if you practice with mild physical fatigue. But mental fatigue can make it hard to get anything useful done, and if you can't concentrate, you are more likely to practice-in mistakes.
You may play better if you catch up on sleep! Groggy, inattentive practice often has to be undone.
I tend to avoid practice when I'm tired. But it is a bad idea!
I find that a 2-hour symphony rehearsal (or concert) - a sort of enforced practice, I suppose - makes me unaware of any tiredness I might have. I sleep well when I get home!
I try to practice daily, but there are some days where the mental exhaustion means that it is not going to work. Those days I just head to bed. The deal with myself is at least I will try.
In all honesty there are things more important than violin. Relationships, making a living and so on. I try to do it every day but it doesn't always happen because I made a trade with something more important. Only a dull boy would say nothing else is ever more important.
I sometimes still practice when I'm dead tired because I don't want to lose what little technique I might actually have. So I'll saw through some less-challenging studies or review old rep. My greatest fear which has come close to happening a few times is that I'll actually fall asleep while playing and drop my beautiful violin.
Try to re-organise your day so that you can do at least 30 minutes (but preferably a full 60 minute routine) in the morning, before anything else.
Is it worth it? Generally, I don't think so.