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

[Bob Dowland]

> 
> 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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> http://q12.org/mailman/listinfo/ode
> 

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