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# Finding velocity vector

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Hello. I wonder if anybody has a good way of finding an arbitrary points velocity vector in a 3d-System where the systems velocity and angular velocity is knowned. The center of the angular velocity is also knowned. I can''t seem to come up with a good way so some help would gladly be recieved :D. /Niklas

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Well, it depends on how your angular speed and center of it are stored... Care to tell us more?

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Sure

The angular velocity is store like this:

Vector angularVelocity;
where the klass Vector has an X, Y and Z. Each for the velocity around that axis.

The center of the angular velocity and the point to check the linear velocity in are also stored in a Vector and is point in the 3d-system.

I guess i want the points linear velocity in the local system caused by the angular velocity and after that convert the new velocity vector to the global system where i add the original systems global speed.

Sorry for being so unspecific,

/Niklas

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I can''t seem to find a good reference online, and I don''t happen to have my mechanics text with me, but I seem to recall that

V = R x W

where V is the velocity vector, W is the angular velocity vector and R is the position vector relative to the origin (through which the W vector passes)

If you get a incorrectly -ve result, swap the order of the R and W

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ok,

Lets say you got the following vectors:

- LinearVelocity

- AngularVelocity (the vector points in the direction of the rotation axis, the length of the vector corresponds to the angular velocity in radians per second)

- Position (position vector of a point relative to the center of the rotation)

the velocity of a point will be:

LinearVelocity + cross product (AngularVelocity, Position)

pretty simple huh?

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Thanks Geoff and SpaceDude. Your formula seems to work fine =). I do the cross product in SpaceDudes order and have the point i check converted into relative coordinants to the center of the rotation.

/Niklas

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