.....|1.....0.......0|

Rx = |0....cosA..sinA|

.....|0...-sinA..cosA|

.....|cosB..0...-sinB|

Ry = |0.....1.......0|

.....|sinB..0....cosB|

.....|cosC...sinC...0|

Rz = |-sinC..cosC...0|

.....|0.......0.....1|

Now we can get Gimbal Lock multiplyig matrices in that order (from left to right): Ry * Rx * Rz, where A = 90 deg. We have:

|1 0 0|

Rx = |0 0 1|

|0 -1 0|

..........|cosB..0...-sinB|...|1...0...0|...|cosB...sinB...0|

Ry * Rx = |0.....1.......0| * |0...0...1| = |0.......0.....1|

..........|sinB..0....cosB|...|0..-1...0|...|sinB..-cosB...0|

...............|cosB...sinB...0|...|cosC...sinC...0|

Ry * Rx * Rz = |0.......0.....1| * |-sinC..cosC...0| =

...............|sinB..-cosB...0|...|0.......0.....1|

..|cosB * cosC - sinB * sinC......cosB * sinC + sinB * cosC.....0|

= |0..........................................0.................1| =

..|sinB * cosC - cosB * sinC......sinB * sinC - cosB * cosC.....0|

**..|cos(B + C)...sin(B + C)...0|**

=

**|0................0........1|**

**..|sin(B + C)..-cos(B + C)...0|**

So, our final matrix is very strange. I thought it should be same as Ry since rotations are the same. Why it difers?

**Edited by Volgogradetzzz, 05 September 2012 - 08:33 AM.**