Clump orientations and their angular velocities

Asked by Tijan

I am a relative novice in using Yade and I have a really simple question. My simulation consists of clumps of spheres and I'm trying to calculate the rotational kinetic energy of the clumps. However it is not clear to me how the orientations of the clumps and their angular velocities are defined. Since the momentums of inertia of clumps are defined in the space of principal axes I would expect also the orientations of clumps to be aligned with the principal axes, but I can't seem to find any documentation on this matter. Regarding the angular velocities - are they defined in the local (principal axes) coordinate system or in the global coordinate system?

Thank you in advance for your help.

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Jan Stránský (honzik) said :
#1

Hello,

> I am a relative novice in using Yade

welcome :-)

> Since the momentums of inertia of clumps are defined in the space of
> principal axes I would expect also the orientations of clumps to be aligned
> with the principal axes, but I can't seem to find any documentation on this
> matter.

it is "moment of inertia" (not momentum). You are right that inertia is
defined in the space of principal axes, let's call it local coordinate
system. So in LCS the inertia tensor T would look like T=diag(inertia).

The orientation is internally stored as a quaternion, but it can be also
transformed to rotation matrix R. It is simply a mapping between local to
global coordinate system. So in GCS the inertia tensor is Rt*T*R. Rt means
transpose of R.

I am afraid that the only documentation is source code itself [1]..

> Regarding the angular velocities - are they defined in the local
> (principal axes) coordinate system or in the global coordinate system?
>
>
angular velocities are in global coordinate system. Be careful if you
wanted to prescribe angular velocity, it would have no effect and one have
to prescribe angular momentum.

cheers
Jan

[1]
http://bazaar.launchpad.net/~yade-pkg/yade/git-trunk/view/head:/core/Clump.cpp

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Bruno Chareyre (bruno-chareyre) said :
#2

For future reference:
Answer #1 refer to the "aspherical" integration scheme [1]. For spheres, or as soon as the "spherical" approximation is used for non-spherical bodies, angular velocity can be prescribed and angular momentum is not used.
Bruno

[1] https://yade-dem.org/doc/formulation.html#orientation-spherical

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