Real-Time Physics Simulation Forum 2012-07-21T21:33:52+00:00 https://pybullet.org/Bullet/phpBB3/app.php/feed/topic/8283 2012-07-21T21:33:52+00:00 2012-07-21T21:33:52+00:00 https://pybullet.org/Bullet/phpBB3/viewtopic.php?p=28358#p28358 <![CDATA[Re: Switch coordinate frame of angular velocity and inertia]]>
The shifting rule says that if a constraint is specified for points g1 and g2 relative to bodies 1 and 2, like this:

a1.dot(p1 + g1) + q1.dot(w1) + a2.dot(p1 + g2) + q2.dot(w2) = c

then the equivalent POR-relative constraint is

a1.dot(p1) + (q1 + g1.cross(a1)).dot(w1) + a2.dot(p2) + (q2 + g2.cross(a2)).dot(w2) = c

This shifting rule correctly trades off linear and angular velocity at the POR. Applying this to the ball-and-socket joing for each u_i gives

u_i.dot(p1) + (g1.cross(u_i)).dot(w1) - u_i.dot(p2) - (g2.cross(u_i)).dot(w2)
I'll go ahead and describe the variables:

a1/u_i = axis/basis vectors
p1/p2 = COM velocities
g1/g2 = vectors pointing from COM to where ball and socket meet
w1/w2 = angular velocities

I should've retyped p1/p2 as v1/v2 but that's how the author has it (with a dot on top). That's about all I know. I'm working on a rag-doll physics system and I didn't need to translate the moment of inertia. Do you have a block solver set up? I recommend reading http://erwincoumans.com/ftp/pub/test/ph ... namics.pdf.

HTH,
Mike

Statistics: Posted by mikeshafer — Sat Jul 21, 2012 9:33 pm

]]> 2012-07-21T19:39:35+00:00 2012-07-21T19:39:35+00:00 https://pybullet.org/Bullet/phpBB3/viewtopic.php?p=28356#p28356 <![CDATA[Switch coordinate frame of angular velocity and inertia]]>
Similar question for inertia tensor 3x3 matrix for 3D rigid body: how to map it from the local CF to a different CF?

My actual use case is to map angular velocity and moment of inertia from the object space to the joint space that is anchored at an offset from the COM of the object.

Thanks!

Statistics: Posted by kingchurch — Sat Jul 21, 2012 7:39 pm

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