How to study a inverse problem? Know the orbit, solve the constraint condition.

Dear all,

Now I face a noval problem, and I do not know how to deal with it, even cannot begin the first step.

As we know, the formulation of a classical mechanical question  is given the initial condition and the constraint condition, and solve the unknown orbit. Now I face a inverse problem. I know the initial condition and the orbit, and would like to solve the unknown constraint condition.

Is there anyone could give some seggestion, I don't know how to do it. Thanks.

Best.