Variable-mass system events. The following derivation is for a body that is gaining mass (accretion). A body of time-varying mass "m" moves at a velocity v at an initial time "t". In the same instant, a particle of mass dm moves with velocity u. The initial momentum can be written as Now at a time "t" + d"t", let both the main body and the particle accrete into a body of velocity v + dv. Thus the new momentum of the system can be written as Since d"m"dv is the product of two small values, it can be ignored, meaning during d"t"
Angular velocity its dual to get a 3 dimensional pseudovector that is precisely the previous angular velocity vector formula_107: Substituting "ω" for "W" into the above velocity expression, and replacing matrix multiplication by an equivalent cross product: It can be seen that the velocity of a point in a rigid body can be divided into two terms – the velocity of a reference point fixed in the rigid body plus the cross product term involving the angular velocity of the particle with respect to the reference point. This angular velocity is the "spin" angular velocity of the rigid body as opposed to