so it has three degrees of freedom; Two particles in space have a combined six degrees of freedom; If two particles in space are constrained to maintain a constant distance from each other, such as in the case of a diatomic molecule, then the six coordinates must satisfy a single constraint equation defined by the distance formula. This reduces the degree of freedom of the system to five, because the distance formula can be used to solve for the remaining coordinate once the other five are specified. Rigid bodies A single rigid body has at most six degrees of freedom (6 DOF) 3T3R consisting of three translations 3T and three rotations 3R. See also Euler angles. For example, the motion of a ship at sea has the six degrees of freedom of a rigid body, and is described as: Translation and rotation: Walking (or surging): Moving forward and backward; Strafing (or swaying): Moving left and right; Elevating (or heaving): Moving up and down; Roll rotation: Pivots side to side; Pitch rotation: Tilts forward and backward; Yaw rotation: Swivels left and right; For example, the trajectory of an airplane in flight has three degrees of freedom and its attitude along the trajectory has three degrees of freedom, for a total of six degrees of freedom. For rolling in flight and ship dynamics, see roll (aviation) and roll (ship motion), respectively. An important derivative is the roll rate (or roll velocity), which is the angular speed at which an aircraft can change its roll attitude, and is typically expressed in degrees per second. For pitching in flight and ship dynamics, see pitch (aviation) and pitch (ship motion), respectively. For yawing in flight and ship dynamics, see yaw (aviation) and yaw (ship motion), respectively. One important derivative is the yaw rate (or yaw velocity), the angular speed of yaw rotation, measured with a yaw rate sensor. Another important derivative is the yawing moment, the angular momentum of a yaw rotation, which is important for adverse yaw in aircraft dynamics. Lower mobility Physical constraints may limit the number of degrees of freedom of a single rigid body. For example, a block sliding around on a flat table has 3 DOF 2T1R consisting of two translations 2T and 1 rotation 1R. An XYZ positioning robot like SCARA has 3 DOF 3T lower mobility. Mobility formula The mobility formula counts the number of parameters that define