about dynamic model of a differential drive system

Hello everyone,

I am working on a middle size (about 40kg) differential drive system. I've already established the kinematics model of it, and now I am continuing work on the dynamics model. Actually, I don't have a good background at physics even the fundamentals. Thus, I felt a little difficult to deal with that. I have some question that I can not answer my self till now. I need your help, and appreciate it very much.

I just think that Kinematics model lets us to operate the robot in a mathematical way. After that had been built, we can drive the robot to move by specifying the velocities in each direction. Thus, it is easy to test that whether a kinematics model is right or not. And it is easy to be build by quoting equations from those published reference papers.

Similarly, it may be easy as well to build a dynamic model of a robot as what we did for the kinematics model, reading papers and quoting equations. However, how can we test a dynamic model? There is one thing that I am wondering. You know, a dynamic model contains the force balance including forces and torques. Thus, I don't know how can I verify it even if we know that we can use a series of correct equations from one paper. Do I need to design a controller? And what is the relationship between kinematics model and dynamics model?

PS: I am using an 3-wheel omnidirectional mobile robot to simulate the 2-wheel differential drive model. It is already a full-fledged robot with APIs. I mean that I need not to do anything for this robot. Thus, what I should do if I want to test a dynamics model of the differential drive system on it.

Thanks very much.