[ODE] matrix

[Thomas Harte]

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>is the rotation matrix unique for ANY combination of
>theta, phi and psi? or do they have their drawbacks?

The rotation matrix is unique for any particular orientation. However, the three angle 
orientation system has singularities, which more or less just means that not all unique 
combinations of theta, phi and psi produce unique orientations. Therefore the rotation 
matrix for a unique theta/phi/psi is not necessarily unique.

However, the rotation matrix method of storing orientations has drawbacks in this 
sense. It is the three angle description that is limited. In fact, ODE is unlikely to be using 
the rotation matrix form internally at all, but intead using quaternions internally then 
converting to orientation matrices when requested because that form is more useful for 
object display. Were it solely using rotation matrices however, the drawbacks would 
include relatively costly rotations (due mostly to having to deal with precision issues) and 
larger than necessary data size.

>are the linear and angular velocities related to euler angles?

No. Linear velocity is exactly the same as if an object could not rotation. So, e.g. a 
velocity vector of (a, b, c) will always mean a units along the global 'x axis', b along the 
global 'y' and c along the global 'z', regardless of object orientation.

Angular velocity has a different meaning again. It is a 3 component vector, which may 
therefore be thought of as describing a direction and a magnitude. The rotation it 
describes is a rotation around the axis described by its rotation of n radians, where n is 
equal to the vector's magnitude. This is a very useful form for calculating how applied 
impulses and forces affect rotation.

-Thomas<P><P>______________________________________________________<BR><a href="http://viral.lycos.co.uk" target="_blank">The making of Brazillian football</a></A><P>


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