Lie on tummy, legs straight and arms bent and flat on floor (as if you would be waving both hands if stood up). Lift your upper body off the floor a few inches and hold, then release and drop down. You can work your upper back too by adding in a straightening of your arms (so arms tight into ears) while your body is raised, then returning them to bent and lying back down. Repeat 10 times and rest. Build up to doing three sets of these, adding more as you get stronger and can do three sets of 15.
I can give you variations on the basic planks too if you want....
Interesting back info...a PT I was speaking to recently said that for each abdominal exercise you do you should do 3 times the number of back strengthening exercises, that is how important your back is! I am definitely guilty of not following this rule though! I guess you only realise when you get back problems
-when in position, dip your lower hip down towards the ground (so you make a v type shape) and then lift back to straight position, repeat as many times as you can manage, aim for three sets of 15-20.
- when in position, raise your upper arm straight so pointing skywards, with palm forward. Then bring it down in front of you and then through the gap underneath you. This tips your body round slightly, working your waist. You can also do this holding a small dumbbell if you want to make it harder.
Both of these can be made (much ) harder by supporting your body on a hand, with straight arm, rather than resting on elbow, same as you can make a full plank harder by using press up position arms.
To make a full plank harder rest one foot on top of the other, or use a bosu ball/Swiss ball to rest your feet. Basically anything which makes it harder to balance - a smaller point of contact such as one foot, or an unstable surface, will make your core work harder.
If you go to the gym, bent over rows with a barbell are great for strengthening your back, just be careful with weight you use with your existing problem. Try maybe 2.5kg on each end and see how you get on, work up if ok.
If you are willing/able to throw cash at this, one of the best pieces of equipment for core and back exercises (and pretty much any other body part) is a TRX suspension trainer, very useful to have at home and to take with you if you travel. You can get one for around £100 on Amazon....lots of vids on YouTube of people using them. I have one and nothing touches it for core strengthening!
Oh I meant to add, I dont do it myself but I think pilates would probably be great for you, but make sure your instructor is aware of your back problem so that he/she can keep a very close eye on your technique so that you don't end up in a worse state.
I do a combined pilates and yoga class which is great for abs, I really feel it doesn't aggravate my sciatica either My evil friend made me lie face down, feet on Swiss ball and one hand each on a medicine ball and then pull Swiss ball in with feet so bum was up in v shape - made total fool of myself falling over