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If I have two "ships", a "daughter" ship lying flat on top of a "mother" ship but with a different heading and both ships are then rotated about the roll and pitch axes of the mother ship, how can I calculate the roll/pitch of the daughter ship from the resulting roll and pitch values of the mothership? The linked image may help to understand what I am asking. The daughter ship is lying flat on the same X-Y plane as the mother ship but is rotated about the Z axis, i.e. it has a different heading. If both ships are then tilted together and I know the roll and pitch of the mother ship, how do I calculate the roll and pitch of the daughter ship? Roll Pitch Calculation

JC_RMB
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  • Hmmm ... Would it be correct to just add the angles together? Surely, if there is only pitching or only rolling, the correct answer is obtained just by adding the angles. – Matti P. Nov 13 '19 at 11:20
  • There's both pitching and rolling and as the daughter ship has a different heading to the mother ship, the pitch and roll axes are different. I cannot simply add them together. – JC_RMB Nov 13 '19 at 11:24
  • Perhaps you should use matrix algebra to solve this problem. Rotation matrices and Euler angles ... – Matti P. Nov 13 '19 at 11:25
  • I've looked into that but most of the information out there seems to suggest that I should apply a sequence of rotations, e.g. rotate about one axis, rotate about a second axis etc.and do them in a certain order. If I am presented with the pitch and roll values of the mother ship, is there a particular sequence I should use to get the values for the daughter ship? – JC_RMB Nov 13 '19 at 11:35
  • The rotation order is very much a convention, every place uses a different one. Your next step is to figure out which rotation order is used. I also wish there was one "universally used" one, but that's sadly not the case. – Matti P. Nov 13 '19 at 11:41

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Just been given this formula by a colleague and it seems to work fine. I'll mark it as an answer for now and it may be useful for someone else in future. If (h) is the heading offset (clockwise rotation) of the daughter ship from the mother ship about the Z axis (alpha in the linked image), (r) is the roll of the mother ship and (p) is the pitch of the mother ship, then;

Daughter ship Roll = $-arcsin(cos(h+90)*sin(p)-sin(h+90)*sin(r))$

Daughter ship Pitch = $arcsin(cos(h)*sin(p)-sin(h)*sin(r))$

JC_RMB
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