Spacetime as a redshift and analyze the effect in terms of scenarios (b) or (d). In classical mechanics, the state of motion of a particle is characterized by its mass and its velocity. Linear momentum, the product of a particle's mass and velocity, is a vector quantity, possessing the same direction as the velocity: p = "mv". It is a "conserved" quantity, meaning that if a closed system is not affected by external forces, its total linear momentum cannot change. In relativistic mechanics, the momentum vector is extended to four dimensions. Added to the momentum vector is a time component that
Angular velocity of bases. For example, changing to the mobile frame: where formula_46 are unit vectors for the frame fixed in the moving body. This example has been made using the Z-X-Z convention for Euler angles. The angular velocity vector formula_47 defined above may be equivalently expressed as an angular velocity tensor, the matrix (or linear mapping) "W" = "W"("t") defined by: This is an infinitesimal rotation matrix. The linear mapping "W" acts as formula_49: A vector formula_51 undergoing uniform circular motion around an axis satisfies: Given the orientation matrix "A"("t") of a frame, whose columns are the moving orthonormal coordinate vectors