Hello to all,(adsbygoogle = window.adsbygoogle || []).push({});

I am currently studying computer graphics and I have came up with the following problem. Consider that we have three coordinate systems, lets say CSA1, CSA2 and CSA3 that have the same origin and differ by a rotation. That is to CSA2 connects to CSA1 by R12 and CSA3 to CSA1 by R13. Assume that Ai represents a base for the corresponding coordinate system CSAi. That is Ai comprises from 3 unit orthogonal vectors that are the base of CSAi. Then A2 connects to A1 via:

A2=R12*A1 (eq. 1)

and moreover

A3=R13*A1 (eq. 2)

eq. 1 becomes A1=inv(R12) * A2 (eq. 3) (inv stands for inverse) and eq. 2 using eq. 3 becomes

A3=R13*inv(R12)*A2 (eq. 4)

now we also know from theory that the coordinates (P1, P2, P3) of a point P in the three coordinates systems are connected via:

P2=inv(R12)*P1 (eq. 5)

P3=inv(R13)*P1 (eq. 6)

eq. 5 becomes P1=R12*P2 and substituting it in eq. 6 we have that

P3=inv(R13)*R12*P2 (eq. 7)

moreover applying the same rule in eq. 4, we get that the coordinates of P in the second and third coordinate system are connected via:

P3=inv(R13*inv(R12))*P2 that is

P3=R12*inv(R13)*P2 (eq. 8)

equations 7 and 8 gives us that

inv(R13)*R12=R12*inv(R13)

which is obviously wrong.

can anyone help me and show me my mistake?

Many thx,

zokos

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Rotation of coordinate system mistake or paradox?

Loading...

Similar Threads - Rotation coordinate system | Date |
---|---|

I Spherical coordinates via a rotation matrix | May 31, 2016 |

2 Rotations on different coordinate systems | Sep 19, 2013 |

Rotation of Gridded Spherical Coordinates to the Same Grid | Feb 18, 2013 |

Converting Rotation matrix to operate on fractional coordinates | Aug 14, 2012 |

Rotations in spherical coordinates | Dec 16, 2010 |

**Physics Forums - The Fusion of Science and Community**