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I'd like to write a program that "simulates" a rigid rod of length L moving in a potential field. The problem is in two dimensions. Friction is assumed to be negligible. The potential field and its gradient is known at every point of the two-dimensional domain.

The "mass" of the rod and the magnitude of the potential gradient can be arbitrarily set. The rod has uniform density.

I understand that the force acting upon a particle in a potential field is -∇P, where P is the potential. This is an attraction of the particle towards lower potentials. What is the force acting on the rod?

Since this is a computer simulation, time and space are discretized. The simulation would proceed in discrete timesteps Δt. How do I compute the position of the rod in each timestep? How would you generally approach this problem?

Your help is greatly appreciated.