How too multiply 2 rotational matrices like this: R(THETA2) . R(THETA1) = R(THETA1 +THETA2) How would that look given the rotation matrix: cos(THETA) -sin(THETA) sin(THETA) COS(THETA)
Last edited by taurus; Sep 19th 2009 at 05:31 AM.
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Originally Posted by taurus How too multiply 2 rotational matrices like this: R(THETA2) . R(THETA1) = R(THETA1 +THETA2) How would that look given the rotation matrix: cos(THETA) -sin(THETA) sin(THETA) COS(THETA) Now use the addition formulas for sine and cosine to see that this is equal to .
Originally Posted by Opalg Now use the addition formulas for sine and cosine to see that this is equal to . how did u get cos(theta1+theta2) from-sin(theta1)sin(theta2)+cos(theta1)cos(theta2)? Shouldnt it be: -cos(theta1-theta2)? and same for the one above that: -sin(theta1-theta2)?
Last edited by taurus; Sep 19th 2009 at 11:00 AM.
Recall that the trigonometrical addition formulae are: "Shouldnt it be: -cos(theta1-theta2)? and same for the one above that: -sin(theta1-theta2)?" So, Hope that helps!
Last edited by Harry1W; Sep 20th 2009 at 03:17 PM. Reason: Improved explanation
But how would you work it out? is it just to memorize? The second column: Thats where am confused.
Originally Posted by taurus But how would you work it out? is it just to memorize? It would be very useful to memorise them; they seem to crop up all the time. There is a nice proof using Euler's formula, if you've ever come across that. Investigate more here Trigonometric Addition Formulas -- from Wolfram MathWorld
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