Response to Dr. Stepan and Dr. Otahal: A mathematical note on the simulations of Codman's Paradox

[...]equations that were used to create the simulations can be formulated using the methods provided in references (Cheng et al., 2000; Cheng, 2000; Cheng, 2004), therefore, interested readers can construct the equations by themselves. [...]inverse of rotation R(a, [theta]) is a rotation of the same angle [theta] about an axis in opposite direction of a, which is described in Eq. By observing the above equations, we know that the R2(a0, β) can be considered as rotation matrix for an axial rotation when the long axis is at the initial position a0. [...]we can replace the first two rotations by the axial rotation and an elevation from a0 to a2 as described in Eq.