Simplified Rolling Calculations: Part 3 The Coupling of Degrees of Freedoms

This paper is the third installment in the series dealing with the rolling motion (and other motions). This paper deals with the
coupling between the degree of freedoms in general and specifically the interaction between the roll with other motions. This
paper attempts to clean the added mass concept(s) from the detrimental errors that are currently used in the establishment implementation and put the theory in the science realm.

     One of main fallacies that plagues the marine engineering is the added mass/moment of inertia implementation such as the
famous fixed 6 × 6 matrix showing the added mass components. This implementation forces a special and strange anomaly equation or view on how added mass should be used. For strange reasons, this implementation was adapted by the establishment without any real questions or challenges. The consequences of his added mass implementation are non logical and counter to the physics that it is known today. For example, the acceleration in one direction causes angular acceleration in another DOF which is not really observed or does not make any sense. Furthermore, this implementation also leads to conceptual inability to reduce the degree of freedom in the model. Where these “coupling” effects (added mass coefficients) go when the number of DOF was reduced? Does this implementation violate the physics laws? To answer this question, this analysis suggests
Something is terribly wrong with the common implementation and it violates Newton’s second law.One of main fallacies that
plagues the marine engineering is the added mass/moment of inertia implementation such as the famous fixed 6 ×6 matrix show-
ing the added mass components. This implementation forces a special and strange anomaly equations or view on how added
mass should be used. For strange reasons, this implementation was adapted by the establishment without any real questions or
challenges. The consequences of this added mass implementation are non logical and counter to the physics that it is known
today. For example, the acceleration in one direction causes angular acceleration in another DOF which is not really observed or
does not make any sense. Furthermore, this implementation also leads to conceptual inability to reduce the degree of freedom in
the model. Where do these “coupling” effects (added mass coefficients) go when the number of DOF is reduced? Does this
implementation violate the physics laws? To answer this question, this analysis suggests something is terribly wrong with the
common implementation and it violates Newton’s second law.

     Here, the belief (in the standard implementation which s used by the vast majority of the industry if not all) is challenged. It was shown that this implementation can not stand any real scrutiny. It was shown that the added mass has only one
whole value for the linear acceleration which can be broken into added mass different components in a different coordinate. The
common implementation fails to explain the change of the added mass and other effects such as geometry effects. For example,
sway does not affect the surge as opposed to the establishment implementation while the pitch and heave affect each other.

     This analysis focuses on the relationship of added mass/added moment of inertia components based on the physical reasoning rather than the non realistic assumption and amorphic mathematical reasoning. It is explained that the connection be-
tween DOFs has three categories which are none, single or both relationships. The none means that the two movements (DOFs)
do not affect each other (living in isolation). The single meaning is that one movement affects others but not the reverse. The
both means that both movements affect each other. Thus, if one wants to move from a fancy realm to a real world one and should
abandon the establishment approach.