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Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In other words, the axis of rotation of a precessing body itself rotates around another axis. A motion in which the second Euler angle changes is called ''nutation''. In physics, there are two types of precession: torque-free and torque-induced. In astronomy, "precession" refers to any of several slow changes in an astronomical body's rotational or orbital parameters, and especially to Earth's precession of the equinoxes. ''(See section Astronomy below.)'' ==Torque-free== In torque-free precession, the angular momentum remains fixed, but the angular velocity vector changes. What makes this possible is a time-varying moment of inertia, or more precisely, a time-varying inertia matrix. The inertia matrix is composed of moments of inertia calculated with respect to separate coordinate axes (e.g. x, y, z), or basis sets. If an object is asymmetric around its principal axis of rotation, the moment of inertia with respect to each basis will change with time, while preserving angular momentum. The result is that the component angular velocities around each axis will vary inversely to each axis' moment of inertia. Poinsot's ellipsoid is a geometrical analog of the functions that govern torque-free motion of a rotating rigid body. The torque-free precession rate of an object with an axis of symmetry, such as a disk, spinning about an axis not aligned with that axis of symmetry can be calculated as follows: : where is the precession rate, is the spin rate about the axis of symmetry, is the moment of inertia about the axis of symmetry, is moment of inertia about either of the other two equal perpendicular principal axes, and is the angle between the moment of inertia direction and the symmetry axis.〔 〕 When an object is not perfectly solid, internal vortices will tend to damp torque-free precession, and the rotation axis will align itself with one of the inertia axes of the body. For a generic solid object without any axis of symmetry, the evolution of the object's orientation, represented (for example) by a rotation 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 counter-acted by repeatedly applying a small rotation vector perpendicular to both and , noting that . Another type of torque-free precession can occur when there are multiple reference frames at work. For example, Earth is subject to local torque induced precession due to the gravity of the sun and moon acting on Earth's axis, but at the same time the solar system is moving around the galactic center. As a consequence, an accurate measurement of Earth's axial reorientation relative to objects outside the frame of the moving galaxy (such as distant quasars commonly used as precession measurement reference points) must account for a minor amount of non-local torque-free precession, due to the solar system’s motion. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Precession」の詳細全文を読む スポンサード リンク
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