[ODE] Moment of Inertia
James Gjerde
jgjerde at contrarymotion.com
Thu Aug 14 09:57:02 2003
This is a multi-part message in MIME format.
------=_NextPart_000_001B_01C36259.BE805A40
Content-Type: text/plain;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
first off this question is not directly related to ode per se, it is =
more of a general physics question and i am asking it here because i am =
assuming there are people on the list who could be of assistance, and i =
do not want to use any part of ode without myself first understanding =
all of the physical concepts.
my question is regarding the inertia tensor for a rigid body, and its =
representation as a 3 by 3 matrix. lets say my body is a uniform cube =
and i initially calculate the moment of inertia in local space where the =
cube is not rotated at all. and assuming the shape and mass never change =
throughout the simulation, the moment of inertia will not change as well =
??=20
my other question would also be since a cube is completely symmetrical =
about each axis, wouldn't it also be true that all the other elements of =
the inertia tensor with exception to the diagonal components would =
always be zero as well? so in theory the moment of inertia ( just for =
the cube ) could be represented really as a vector, or in the case of a =
cube, actually a scalar since all of the components would have the same =
value and the force or torque acting on the body would have to be =
transformed into the object's local coordinate system. i am assuming =
though it is common practice to transform the tensor into world space =
coords since that is how in a simulation forces are represented and i =
guess this is what is confusing me. i would appreciate it very much if =
someone could tell me if i am understanding this correctly or if i am =
off, i am learning this all on my own reading books and looking at =
websites and i have no other references.
james
------=_NextPart_000_001B_01C36259.BE805A40
Content-Type: text/html;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Diso-8859-1">
<META content=3D"MSHTML 6.00.2800.1170" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT face=3DArial size=3D2>first off this question is not directly =
related to ode per se, it is more of a general physics question and =
i am=20
asking it here because i am assuming there are people on the list who =
could be=20
of assistance, and i do not want to use any part of ode without myself =
first=20
understanding all of the physical concepts.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial size=3D2>my question is regarding the inertia =
tensor for a=20
rigid body, and its representation as a 3 by 3 matrix. lets say my body =
is a=20
uniform cube and i initially calculate the moment of inertia in local =
space=20
where the cube is not rotated at all. and assuming the shape and mass =
never=20
change throughout the simulation, the moment of inertia will not change =
as well=20
?? </FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT><FONT face=3DArial =
size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial size=3D2>my other question would also be since a =
cube is=20
completely symmetrical about each axis, wouldn't it also be true that =
all the=20
other elements of the inertia tensor with exception to the diagonal =
components=20
would always be zero as well? so in theory the moment of inertia ( just =
for the=20
cube ) could be represented really as a vector, or in the case of a =
cube,=20
actually a scalar since all of the components would have the same value =
and the=20
force or torque acting on the body would have to be transformed into the =
object's local coordinate system. i am assuming though it is common =
practice to=20
transform the tensor into world space coords since that is how in a =
simulation forces are represented and i guess this is what is confusing=20
me. i would appreciate it very much if someone could tell me =
if i am=20
understanding this correctly or if i am off, i am learning this all on =
my own=20
reading books and looking at websites and i have no other=20
references.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial size=3D2>james</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV></BODY></HTML>
------=_NextPart_000_001B_01C36259.BE805A40--