[overture] Re: Rigidbody Torque / angular acceleration
- From: "#DOMINIC DENVER JOHN CHANDAR#" <DOMI0002@xxxxxxxxxx>
- To: <overture@xxxxxxxxxxxxx>
- Date: Fri, 20 Jun 2008 23:43:36 +0800
Thanks Bill..
Also ..I see that both the versions are the same for a 2D case....
Dominic
-----Original Message-----
From: overture-bounce@xxxxxxxxxxxxx
[mailto:overture-bounce@xxxxxxxxxxxxx] On Behalf Of Bill Henshaw
Sent: Friday, June 20, 2008 11:24 PM
To: overture@xxxxxxxxxxxxx
Subject: [overture] Re: Rigidbody Torque / angular acceleration
Hi Dominic,
These are Euler's equations, see
http://en.wikipedia.org/wiki/Euler%27s_equations
...Bill
#DOMINIC DENVER JOHN CHANDAR# wrote:
> Hi Bill,
>
> In OverBlown v21, the code RigidBodyMotion.C had the following
> lines to compute the angular acceleration from the torque as :
>
> for( axis=0; axis<3; axis++ )
> {
> omegaDot(axis)=(
> (1.-alpha)*(
> g(0,ip1)*e(0,axis,ip1)
> +g(1,ip1)*e(1,axis,ip1)
> +g(2,ip1)*e(2,axis,ip1))
>
> +alpha *(
> g(0,i)*e(0,axis,i)
> +g(1,i)*e(1,axis,i)
> +g(2,i)*e(2,axis,i))
> )/mI(axis);
> }
>
> /So this is equivalent to the statement G dot e_i = mI_i
> \omegaDot_i (From Newtons Laws). /
>
> whereas in cg.v22, the same code is as follows :
>
> for( axis=0; axis<3; axis++ )
> {
> const int axisp1=(axis+1) % 3;
> const int axisp2=(axis+2) % 3;
>
> omegaDot(axis)=(
> (1.-alpha)*(
> (mI(axisp1)-mI(axisp2))*w(axisp1,ip1)*w(axisp2,ip1)+
> g(0,ip1)*e(0,axis,ip1)+
> g(1,ip1)*e(1,axis,ip1)+
> g(2,ip1)*e(2,axis,ip1))
>
> +alpha *(
> (mI(axisp1)-mI(axisp2))*w(axisp1,i)*w(axisp2,i)+
> g(0,i)*e(0,axis,i)+
> g(1,i)*e(1,axis,i)+
> g(2,i)*e(2,axis,i))
> )/mI(axis);
> }
>
>
> Now, both versions look alike except for the additional term in
> cg.v22 - " (mI(axisp1)-mI(axisp2))*w(axisp1,ip1)*w(axisp2,ip1) " ~
> (I2-I3)*w2*w3 ..
> I'd like to know the basis for adding this term...
>
> Regards,
> Dominic
>
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