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
Variable-mass system to the center of mass of the body, and v is the velocity of the body. In astrodynamics, which deals with the mechanics of rockets, the term "v" is often called the effective exhaust velocity and denoted "v". There are different derivations for the variable-mass system motion equation, depending on whether the mass is entering or leaving a body (in other words, whether the moving body's mass is increasing or decreasing, respectively). To simplify calculations, all bodies are considered as particles. It is also assumed that the mass is unable to apply external forces on the body outside of accretion/ablation