# [ODE] Is it possible to Scale a given Inertia-Matrix?

Bob Dowland Bob.Dowland at blue52.co.uk
Thu Jun 17 11:03:02 MST 2004

```>
> Weren't computers supposed to be doing all this math for us by now?
>
> ;-)
>

Yeah - gone are the days where the papers and pencils ran our lives!

=:0

> -----Original Message-----
> From: GARY VANSICKLE [mailto:g.r.vansickle at worldnet.att.net]
> Sent: 17 June 2004 03:51
> To: ode at q12.org
> Subject: RE: [ODE] Is it possible to Scale a given Inertia-Matrix?
>
>
> > Ixx = SUMi (mi * (yi^2 + zi^2))
> > Iyy = SUMi (mi * (xi^2 + zi^2))
> > Izz = SUMi (mi * (xi^2 + yi^2))
> > Ixy = - SUMi ( mi * xi * yi )
> > Ixz = - SUMi ( mi * xi * zi )
> > Iyz = - SUMi ( mi * yi * zi )
> >
> > assume:  xi = scalex * nxi,  yi = scaley * nyi, zi = scalez * nzi
> >
> > so the simplier version  :) is :
> > Ixx = SUMi (mi * (scaley^2 nyi^2 + scalez^2 * nzi^2))
> > Iyy = ..
> > Izz = ..
> > Ixy = - SUMi (mi * scalex * nxi * scaley * nyi)
> > Iyz =
> > Ixz = ...
> >
> > "I" can only be scale when "scalex == scaley == scalez  ==
> scale" because
> > of
> > Ixx, Iyy, Izz square xi,yi,zi
> >
> > NewIxx = scale^2 Ixx
> > NewIyy = scale^2 Iyy
> > NewIzz = scale^2 Izz
> > NewIxy = scale^2 Ixy
> > NewIxz = scale^2 Ixz
> > NewIyz = scale^2 Iyz
> >
> > ---------------------------------
> > OR: the extended :) version
> >
> > Ixx = SUMi (mi * (yi^2 + zi^2)) = SUMi (mi * yi^2) + SUMi
> (mi * zi^2) = b
> > +
> > c
> > Iyy = SUMi (mi * (xi^2 + zi^2)) = a + c;
> > Izz = SUMi (mi * (xi^2 + yi^2)) = a + b;
> >
> > Ixy = - SUMi (mi * oldscalex * nxi * oldscaley * nyi)
> > Iyz =
> > Ixz = ...
> >
> > compute a,b,c - solve linear set of equations
> >
> > and apply the new scale:
> >
> > NewIxx = nscaley^2 * b + nscalez^2 * c
> > NewIyy = nscalex^2 * a + nscalez^2 * c
> > NewIzz = nscalex^2 * a + nscaley^2 * b
> > NewIxy = nscalex * nscaley * Ixy;
> > NewIyz = nscaley * nscalez * Iyz;
> > NewIxz = nscalex * nscalez * Ixz;
> >
> > Petr Sovis
> >
> > P.S. I hope, I'm right. Otherwise, sorry for mislead.
>
> Weren't computers supposed to be doing all this math for us by now?
>
> ;-)
>
> --
> Gary R. Van Sickle
>
>
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> ODE at q12.org
> http://q12.org/mailman/listinfo/ode
>

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