Suppose you have a weightless rod with at the endpoints two masses. This is a special rod whose length varies in time as a function L(t). If I consider this rod in free fall my intuition is that this rod will rotate for suitable L(t). However, I want to write down the equations of motions for this rod. I am not so sure how to do this in the sense of what kind of coordinates are useful and which physics formulas I should consider. Any help is welcome.