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
Linear belief function is a special type of belief function in the sense that its focal elements are exclusive, parallel sub-hyperplanes over the certainty hyperplane and its mass function is a normal distribution across the sub-hyperplanes. Based on the above geometrical description, Shafer and Liu propose two mathematical representations of a LBF: a wide-sense inner product and a linear functional in the variable space, and as their duals over a hyperplane in the sample space. Monney proposes still another structure called Gaussian hints. Although these representations are mathematically neat, they tend to be unsuitable for knowledge representation in expert systems. A linear belief