Pull-ups mainly work the lats -- if you want to work those, your best bet might be to grab some cheap resistance bands and do lat pull-downs. Or do pull-overs if you've got some light weights.
If you want to strengthen your lower back, there are lots of bodyweight exercises you can do, mostly variations on the yoga locust pose. If you've got a Swiss ball and somewhere to wedge your feet, you can do full back hyperextensions.
If you're interested in general-purpose core stability: planks planks planks *g*.
(I know I've just thrown a lot of exercise names at you -- let me know what you're interested in, and I can provide more details.)
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Pull-ups mainly work the lats -- if you want to work those, your best bet might be to grab some cheap resistance bands and do lat pull-downs. Or do pull-overs if you've got some light weights.
If you want to strengthen your lower back, there are lots of bodyweight exercises you can do, mostly variations on the yoga locust pose. If you've got a Swiss ball and somewhere to wedge your feet, you can do full back hyperextensions.
If you're interested in general-purpose core stability: planks planks planks *g*.
(I know I've just thrown a lot of exercise names at you -- let me know what you're interested in, and I can provide more details.)