Search results
Results from the WOW.Com Content Network
They constitute a mixed axes of rotation system, where the first angle moves the line of nodes around the external axis z, the second rotates around the line of nodes N and the third one is an intrinsic rotation around Z, an axis fixed in the body that moves. The static definition implies that: α (precession) represents a rotation around the z ...
The most external matrix rotates the other two, leaving the second rotation matrix over the line of nodes, and the third one in a frame comoving with the body. There are 3 × 3 × 3 = 27 possible combinations of three basic rotations but only 3 × 2 × 2 = 12 of them can be used for representing arbitrary 3D rotations as Euler angles.
They constitute a mixed axes of rotation system, where the first angle moves the line of nodes around the external axis z, the second rotates around the line of nodes and the third one is an intrinsic rotation around an axis fixed in the body that moves. These rotations are called precession, nutation, and intrinsic rotation.
The most common of them is the NASA / NORAD "two-line elements" (TLE) format, [4] originally designed for use with 80 column punched cards, but still in use because it is the most common format, and 80-character ASCII records can be handled efficiently by modern databases.
The rate of precession depends on the inclination of the orbital plane to the equatorial plane, as well as the orbital eccentricity.. For a satellite in a prograde orbit around Earth, the precession is westward (nodal regression), that is, the node and satellite move in opposite directions. [1]
The rotation group is a Lie group of rotations about a fixed point. This (common) fixed point or center is called the center of rotation and is usually identified with the origin. The rotation group is a point stabilizer in a broader group of (orientation-preserving) motions. For a particular rotation: The axis of rotation is a line of
The longitude of the ascending node, also known as the right ascension of the ascending node, is one of the orbital elements used to specify the orbit of an object in space. Denoted with the symbol Ω , it is the angle from a specified reference direction, called the origin of longitude , to the direction of the ascending node (☊), as ...
Euler angles for Body 3-1-3 Sequence – The xyz (original fixed Lab) system is shown in blue, the XYZ (rotated final Body) system is shown in red. The line of nodes, labelled N and shown in green, is the intermediate Body X-axis around which the second rotation occurs.