I shake whenever I have to use my core muscles, like when doing ab work. I don't have that problem with any other body part, but I've developed the muscles on those body parts. As I continued to work my core over the months, the shaking occurred less often and less violently. I think you just have to keep at it until you strengthen the muscles that are shaking.

At worst it's only embarrassing to shake because it shows you are weak but who cares. That's why you're there... to get stronger.