Significant wave energy conversion may be achieved with multiple floats with several modes of motion combining constructively to generate power. With the M4 system, power take off is at hinges to absorb resulting pitch motions. Complexity increases with number of floats and conventional vectorial multi-body dynamics may be conveniently replaced by the recently formulated moving frame method based on the calculus of variations to avoid free-body diagrams and joint reaction forces. Furthermore by utilising group theory to gather spatial rotations and angular velocities in a common structure, the obtained notation is general and straight-forward to apply for single and multi-body systems. This paper lays the foundations for incorporating hydrodynamic forces into the moving frame method. The method is applied to 3, 6 and 8 float cases in regular and irregular waves with results compared to the vectorial method and experimental measurements, showing close agreement. It is suggested that this is a more natural and general approach for complex multi-body, multi-hinge hydrodynamics systems.