Line theory: Line local orientation

At any point $P$, the line orientation is defined by its local axes $\mat{P}\urm{xyz}$. $P\urm{z}$ is in the axial direction, towards end B, and is determined by the azimuth and declination angles; $P\urm{x}$ and $P\urm{y}$ are normal to the line axis.

At the ends of the line, these local axes are referred to as the end axes $\Exyz$, and their directions are specified by the end orientation angles on the line data form.

At points on the line other than the ends, the calculation of the local orientation depends on whether torsion is included:

If torsion is included then the local $\mat{P}\urm{xyz}$ directions are calculated using the specified torsional properties of the line.
If torsion is not included then the local directions at $P$ are calculated by assuming that no twisting occurs anywhere along the line between end A and $P$. OrcaFlex starts with the orientation at end A (as specified by its end orientation angles), and steps along the line from node to node, using the no-twist assumption at each step to calculate the next node's local orientation, up to point $P$.

Note:

If end A is free or if it is released then the local orientations are calculated as if end A was connected to an object aligned with the global axes. You should therefore exercise caution when interpreting results which depend on the local orientations of the line in these cases.