Cross product "matrix", then it can be generalized in an arbitrary number of dimensions. In mechanics, for example, the angular velocity can be interpreted either as a pseudovector formula_167 or as a anti-symmetric matrix or skew-symmetric tensor formula_168. In the latter case, the velocity law for a rigid body looks: where Ω is formally defined from the rotation matrix formula_170 associated to body's frame: formula_171 In three-dimensions holds: In quantum mechanics the angular momentum formula_173 is often represented as an anti-symmetric matrix or tensor. More precisely, it is the result of cross product involving position formula_174 and linear momentum formula_111: Since both
Rigid body forward with respect to their own orientation. Then, if the body follows a closed orbit in a plane, the angular velocity integrated over a time interval in which the orbit is completed once, is an integer times 360°. This integer is the winding number with respect to the origin of the velocity. Compare the amount of rotation associated with the vertices of a polygon. Any point that is rigidly connected to the body can be used as reference point (origin of coordinate system "L") to describe the linear motion of the body (the linear position, velocity and acceleration vectors depend