Rigid body dynamics r and velocities v. Select a reference point R and compute the relative position and velocity vectors, The total linear and angular momentum vectors relative to the reference point R are and If R is chosen as the center of mass these equations simplify to To specialize these formulas to a rigid body, assume the particles are rigidly connected to each other so P, i=1...,n are located by the coordinates r and velocities v. Select a reference point R and compute the relative position and velocity vectors, where ω is the angular velocity of the system. The linear momentum and
Angular velocity with a linear velocity "V"("t") in each instant. To obtain the equations, it is convenient to imagine a rigid body attached to the frames and consider a coordinate system that is fixed with respect to the rigid body. Then we will study the coordinate transformations between this coordinate and the fixed "laboratory" system. As shown in the figure on the right, the lab system's origin is at point "O", the rigid body system origin is at and the vector from "O" to is R. A particle ("i") in the rigid body is located at point P and the vector position