[ODE] Angular velocity

[Yefei He]

Hi, 

    I think Left handed rule explains my problem. So this means a positive 
angle rotates the object clockwise since rotation is in a left-handed 
coordinate system. My problem is then, how are the angles in the function 
dRFromEulerAngles( R, phi, theta, psi ) interpreted? I use it to set the 
rotation angles. I did a comparison of this to dRFromAxisAngle( R, ax, ay, 
az, angle ). And I noticed the differences in the rotation matrix that 
they generate: 

    dRFromEulerAngles( R, a, 0, 0 ) 
    1       0       0
    0    cos(a)  sin(a)
    0   -sin(a)  cos(a)

    dRFromEulerAngles( R, 0, a, 0 )
 cos(a)     0   -sin(a)
    0       1       0
 sin(a)     0    cos(a)

    dRFromEulerAngles( R, 0, 0, a )
 cos(a)  sin(a)     0
-sin(a)  cos(a)     0
    0       0       1

and
    dRFromAxisAngle( R, 1, 0, 0, a )
    1       0       0
    0    cos(a) -sin(a)
    0    sin(a)  cos(a)

    dRFromAxisAngle( R, 0, 1, 0, a )
 cos(a)     0    sin(a)
    0       1       0
-sin(a)     0    cos(a)

    dRFromAxisAngle( R, 0, 0, 1, a )
 cos(a) -sin(a)     0
 sin(a)  cos(a)     0
    0       0       1

    That means Euler angles need to be negated to match the results of 
rotation around x, y, or z axis. The discrepancy between Euler angles 
and angular velocity is the same. My next question is then, is there a 
reason why Euler angles are interpreted this way in ODE? I thought 
in the left-handed system, A positive Euler angle would also mean a 
clockwise rotation around axis? 

    Yefei 

> -----Original Message-----
> From: Daniel Monteiro Basso [mailto:dmbasso at inf.ufrgs.br]
> Sent: Wednesday, April 13, 2005 5:16 PM
> To: Yefei He
> Subject: Re: [ODE] Angular velocity
> 
> 
> 
> The convention for rotations in ODE is the "left hand rule": the thumb 
> point to the positive side of the axis, the other fingers show the 
> direction of the rotation for a positive value. If I'm mistaken, 
> please let me know...
> 
> Cheers,
> 
> Daniel
>