Muscles are made up of many fibers. When a muscle is used, not all the fibers contract at the same time. Some rest while the others work, and then they trade places. When the muscles are really challenged, the changeovers can get a little ragged.
Beginning yogis often shake quite a lot. As muscles get stronger from regular practice, the fibers learn to trade off between firing and resting with smoother coordination. Eventually quivering often subsides (though there will always be teachers who turn students into yoga jelly, independent of their strength).
To calm the body, try to hug the quivering (contracting) muscle against its underlying bone and press the bone into the muscle being stretched.
Quivering is not necessarily bad, but it may be a sign that the body is overworked. Several years ago, when slugger Mark McGwire was mired in a terrible slump, a sportscaster asked Mac’s hitting coach what the problem was. The coach opined that McGwire was trying too hard, and needed to “try easier.”
Tune into the brain, the eyes, the root of the tongue, and, most of all, the breath. If any of these areas feel hard or constricted, take the coach’s advice: Try easier.