Mass in special relativity the mass of a moving particle." When the relative velocity is zero, formula_33 is simply equal to 1, and the relativistic mass is reduced to the rest mass as one can see in the next two equations below. As the velocity increases toward the speed of light "c", the denominator of the right side approaches zero, and consequently formula_33 approaches infinity. In the formula for momentum the mass that occurs is the relativistic mass. In other words, the relativistic mass is the proportionality constant between the velocity and the momentum. While Newton's second law remains valid in the form the
Angular velocity Lie algebra of the Lie group of rotations of an "n"-dimensional inner product space. In three dimensions, angular velocity can be represented by a pseudovector because second rank tensors are dual to pseudovectors in three dimensions. Since the angular velocity tensor "W" = "W"("t") is a skew-symmetric matrix: its Hodge dual is a vector, which is precisely the previous angular velocity vector formula_60. If we know an initial frame "A"(0) and we are given a "constant" angular velocity tensor "W", we can obtain "A"("t") for any given "t". Recall the matrix differential equation: This equation can be integrated to give: