# [ODE] Angular velocity

Thu Apr 14 12:22:37 MST 2005

```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,