N-body problem of first-order differential equations, with initial conditions as initial position coordinates and initial momentum values. Symmetries in the -body problem yield global integrals of motion that simplify the problem. Translational symmetry of the problem results in the center of mass moving with constant velocity, so that , where is the linear velocity and is the initial position. The constants of motion and represent six integrals of the motion. Rotational symmetry results in the total angular momentum being constant where × is the cross product. The three components of the total angular momentum yield three more constants of the motion. The
Constant linear velocity Constant linear velocity In optical storage, constant linear velocity (CLV) is a qualifier for the rated speed of an optical disc drive, and may also be applied to the writing speed of recordable discs. CLV implies that the angular velocity (i.e. rpm) varies during an operation, as contrasted with CAV modes. The concept of constant linear velocity was patented in 1886 by phonograph pioneers Chichester Bell and Charles Tainter. Laserdiscs, the first consumer optical discs, used constant linear velocity to double playback time (CLV / "extended play" discs can hold 1 hour per side; CAV / "standard play" discs can