How Do You Change Sleep?

Do you know about circadian rhythms? I've read all the books on sleep and talked to my doctor etc etc but I guess I just don't get this part. Maybe it is more a philosophical question. Here goes. I fall asleep happily about 10 or 11 at night. I've had a decent day with activities, exercise healthy food, no caffeine after 2 p.m. and so forth. Then about 3 in the morning I wake up happy and full of energy. I've kind of given in to it i.e. just start doing stuff and keeping busy. But it is kind of messing up my life because later I'm tired, want naps etc. I do have some other health issues but I've been over and over this with my doc and nothing there. By the way I am not interested in using pills for sleep. Does anybody else deal with this or have some innovative practical strategies? It doesn't feel like insomnia, it's more like interruption. Thoughts or suggestions? Thanks!