Friday, June 11, 2010

Partition of Unity Detailed - Greg Egan

"The surface of a hypersphere in 5 dimensions can be described by the equation:
x2 + y2 + z2 + u2 + w2 = R2 (1)

where x,y,z,u,w are the 5 spatial coordinates, and the origin of the coordinate system lies at the centre of the hypersphere.

Suppose this hypersphere is rotating as a rigid body. In general (in any number of dimensions) the velocity v of any point of a rotating body is given by the product of the body's angular velocity matrix, Ω, with the vector for the point in question, r.
v = Ω r"

5 out of 5

No comments:

Post a Comment