I want to know the motion pattern of two objects that spin around each other,for example, me and my friend spin around each other,I look at her and see she is spining around me and she look at me and see that I spining around her.
What exactly is your question? Let's say that you and your friend are on a frictionless sheet of ice, holding hands and spinning around each other. In that case you can describe the motion as both of you spinning around your common center of mass, while that center of mass may itself be moving. True, from your point of view (a noninertial frame) she is spinning around you, and vice versa.