matrix that transforms internal to external coordinates, may be numerically simulated. Given the object's fixed internal moment of inertia tensor and fixed external angular momentum , the instantaneous angular velocity is Precession occurs by repeatedly recalculating and applying a small rotation vector for the short time ; e.g.: for the skew-symmetric matrix . The errors induced by finite time steps tend to increase the rotational kinetic energy: this unphysical tendency can be counteracted by repeatedly applying a small rotation vector perpendicular to both and , noting that Torque-induced Torque-induced precession (gyroscopic precession) is the phenomenon in which the axis of a spinning object (e.g., a gyroscope) describes a cone in space when an external torque is applied to it. The phenomenon is commonly seen in a spinning toy top, but all rotating objects can undergo precession. If the speed of the rotation and the magnitude of the external torque are constant, the spin axis will move at right angles to the direction that would intuitively result from the external torque. In the case of a toy top, its weight is acting downwards from its center of mass and the normal force (reaction) of the ground is pushing up on it at the point of contact with the support. These two opposite forces produce a torque which causes the top to precess. The device depicted on the right (or above on mobile devices) is gimbal mounted. From inside to outside there are three axes of rotation: the hub of the wheel, the gimbal axis, and the vertical pivot. To distinguish between the two horizontal axes, rotation around the wheel hub will be called spinning, and rotation around the gimbal axis will be called pitching. Rotation around the vertical pivot axis is called rotation. First, imagine that the entire device is rotating around the (vertical) pivot axis. Then, spinning of the wheel (around the wheelhub) is added. Imagine the gimbal axis to be locked, so that the wheel cannot pitch. The gimbal axis has sensors, that measure whether there is a torque around the gimbal axis. In the picture, a section of the wheel has been named . At the depicted moment in time, section is at the perimeter of the rotating motion around the (vertical) pivot axis. Section , therefore, has a lot of angular rotating velocity with respect to the rotation around the pivot axis, and as is forced closer