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 run about 2.5 times as fast when recording at the inner rim of the disc as on the outer rim. Some high-speed recorders use the zoned CLV method (ZCLV), which divides the disc into stepped zones, each of which has its own constant linear velocity. At higher speeds, ZCLV offers a compromise between CAV, which enables faster seek times, and CLV, which enables greater storage capacity. A ZCLV recorder rated at "52X", for example, would write at 20X on the innermost zone and then progressively step up to 52X at the outer rim. Constant Angular Acceleration (CAA) is a variant