Your core strength is a very important aspect of your physique if you want to throw people with any throw involving rotating your shoulders. Whenever you are doing Judo you are always using your core to stabilize and transfer power from your lower body into your upper body. Here are a few ways you can incorporate your core into your strength and conditioning programs.
Think about it:
I watch so many athletes and trainers train a particular body part and they are only concentrating on the muscle they are working. For example you may be performing a bench press and although it is a chest exercise you are still working your core muscles to stabilize yourself. I am constantly telling my clients to contract their core before lifting any weights. This will not only give you a better workout but it will also give you a stronger core when lifting.
You must not neglect the use of squats, dead lifts and overhead pressing movement in your strength programs. All of these movements utilize a lot of core strength and stabilizing muscles which are a must when training for judo. These exercises if done properly can seriously increase your strength and power. Just make sure you are lifting with the correct technique.
Whenever someone hurts their back it is always when they are twisting or turning to get something. Judo is also a rotational strength sport therefore it is crucial that you include rotational core exercises into your strength program besides the usual plank and crunches. Include Russian twists, barbell twists, wrestler twists and other twisting exercises in your strength training regime.
Unilateral training sounds impressive but it is simply training one side at a time opposed to both at the same time. For example instead of doing dumbbell bench press with a dumbbell in both hands perform the movement with a dumbbell in only one hand. This will force your core to activate and stabilize harder because you are now unbalanced. You can do this with exercises such as dumbbell incline and decline bench press, dumbbell shoulder press and overhead presses.
I also highly recommend performing pelvic floor exercises as a way to increase your core strength. In order to get familiar with using your pelvic floor muscles I suggest you see a sports physiotherapist to assist you in getting the right contraction as it is fairly strange at the beginning.