Note on Why GZ is Fundamentally Not Righting Arm

The righting arm is a fundamental quantity that controls the rolling and pitching motions and is required to write the governing equations. Using the Lagrangian mechanics (as opposed to Newtonian mechanics), it was shown that the righting arm is not GZ . For over 200 years, engineers have described the righting arm for the roll and pitch simply by GM sin θ as obvious and simple. The physics dictates that the torque is made from two skewed identical forces times the distance between these forces. In this case, like everything in marine engineering, the establishment's ideas in marine engineering are wrong. This erroneous idea is typical of all the errors in the field. Yet, the distance between these two forces is based on Bouguer’s diagram, which has a major error which actually was well known even to Bouguer. Recently, the correct distance was found using the Lagrangian method. Currently, this distance interpretation is done using the standard Newtonian mechanics. The wrong distance between the couple forces rendered almost all the research work based on the previous idea, at best, useless. All the calculations based on the establishment's model GZ have to be disregarded.