[ODE] moment of inertia

Dan Riley dpriley at ucla.edu
Mon May 20 20:55:02 2002


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ok im just starting to build articulated body dynamics into a program im =
writing, however, i would like to build the engine myself ( i like to =
know exactly how everything works in the program and would like to =
custom tailor it to what i already know and want), however, my phsyics =
skills are not the best (im a sophomore in college studying design). =
I've read through featherstone's "robot dynamics algorithms" but If some =
of you could answer some of the following questions that would be great.

I'll start off with some simple ones:

moment of inertia:
the rigid bodies in my program are all just blocks with uniform density. =
from what I understand, this should mean that the moment of inertia =
matrix for each body should be as follows:

Ixx =3D (m/12)*(height^2+length^2)
Iyy =3D     "    *(length^2+width^2)
Izz =3D     "    *(height^2+width^2)

matrix is then
{  Ixx,   0 ,   0 ,
    0  , Ixy,   0 ,
    0  ,  0  ,  Ixz}

is this correct?


do you guys mind if I ask more questions?

Dan


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<DIV><FONT face=3DArial size=3D2>ok im just starting to build =
articulated body=20
dynamics into a program im writing, however, i would like to build the =
engine=20
myself ( i like to know exactly how everything works in the program and =
would=20
like to custom tailor it to what i already know and want), however, my =
phsyics=20
skills are not the best (im a sophomore in college studying design). =
I've read=20
through featherstone's "robot dynamics algorithms" but If some of you =
could=20
answer some of the following questions that would be great.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>I'll start off with some simple =
ones:</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>moment of inertia:</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>the rigid bodies in my program are all =
just blocks=20
with uniform density. from what I understand, this should mean that the =
moment=20
of inertia matrix for each body should be as follows:</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>Ixx =3D =
(m/12)*(height^2+length^2)</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>Iyy=20
=3D&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"&nbsp;&nbsp;&nbsp;=20
*(length^2+width^2)</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>Izz =3D&nbsp;&nbsp;&nbsp;&nbsp; =
"&nbsp;&nbsp;&nbsp;=20
*(height^2+width^2)</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>matrix is then</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>{&nbsp; Ixx,&nbsp;&nbsp;&nbsp;0 =
,&nbsp;&nbsp; 0=20
,</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>&nbsp;&nbsp;&nbsp; 0&nbsp; , =
Ixy,&nbsp;&nbsp; 0=20
,</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>&nbsp;&nbsp;&nbsp; 0&nbsp; ,&nbsp; =
0&nbsp; ,&nbsp;=20
Ixz}</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>is this correct?</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>do you guys mind if I ask more=20
questions?</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>Dan</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV></BODY></HTML>

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