Actually, when posting, you should be rising from both the knee and the foot. If you rise only from your knee, you may have no anchor into your stirrup, if you rise only from your foot, your knee may rotate out , off the saddle and you will be "jack in the boxing". Smooth contact of leg from thigh to mid calf, is optimal. Your hip will "open and close " because you do lever off you your knee somewhat, but if your weight goes only to the knee and is Pinned against the saddle there, you whole lower leg is pretty useless.
I like to remember that the ideal is that if your horse disappeared from under you , would you be able to land in a standing position and stick your landing, like a gymnast doing a dismount? If you were standing, in the position of pretenting to be horseback and posting, than what muscles do you use to rise and fall? Aboard the horse it will be pretty close, except that since the space between your legs is not air, you will be pushing more again this mass, and moving mass, rather than air (in your pretend position) and will generate energy in your rebound off of the horse.
Sorry, I sound like Mr. Science here. One beer with dinner and I'm off and talking . . . . .