Automatic air hockey

Question

Mathematics

What mathematical apparatus should be used to create a mat. air hockey model with one of the impact pucks controlled by an external force?
Suppose we know the external force acting on one of the impact washers, the mass of the washer and two impact washers.
There is a lot of garbage on the Internet, maybe someone has already done calculations and built a checkmate. model will be very grateful. Interesting for purely personal purposes.