When I started Judo/jiujitsu I was wiped after class for the first month or so, but we were doing a fair amount of sparring. Prior to that I was hitting the gym, doing alot of striking MA etc... but the nature of grappling works you in different ways.
You'll probably find your grip strength taxed from all the gi-grabbing and your shoulders/chest/back will likely be the most fatigued.
Remember to relax, take it easy at first and don't work with much power - get technique down first and last. The less power you have to rely on the better. Beginners always compensate for a lack of technique with brute strength, so when you get tired don't sweat it. It's all part of the process. You'll gradually learn how to roll relaxed all the while getting stronger.
Enjoy!
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ask your doctor if getting off your ass is right for you!
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