This implies a different definition for the line of nodes.

The X-axis now lies on the line of nodes.

The middle matrix represent a rotation around an intermediate axis called line of nodes.

The Z-axis is now in its final orientation, and the X-axis remains on the line of nodes.

There is a similar construction for , projecting it first over the plane defined by the axis z and the line of nodes.

For the orbit of the Earth around the Sun is important the line of nodes formed by the ecliptic and the equator.

The line of nodes is the intersection of the object's orbital plane with the plane of reference.

For circular orbits with zero inclination the argument of latitude is also undefined, because there is no uniquely determined line of nodes.

The line of nodes (N) is defined as the intersection of the xy and the XY coordinate planes.

For the above-listed sequence of rotations, the line of nodes N can be simply defined as the orientation of X after the first elemental rotation.

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.

Seen from far, we can also see dark and pale lines: the pale lines correspond to the lines of nodes, that is, lines passing through the intersections of the two patterns.

The line of its apses precesses gradually with a period of roughly 8.85 years, while its line of nodes turns a full circle in roughly double that time, 18.6 years.

The geometrical definition (referred sometimes as static) of the Euler angles is based on the axes of the above-mentioned (original and rotated) reference frames and an additional axis called the line of nodes.

The orbital planes cross each year at a line of nodes resulting in at least two, and up to five, solar eclipses occurring each year; no more than two of which can be total eclipses.

The two points at which Moon's path crosses the Sun's Ecliptic are known as the nodes, shown as N1 and N2, and the line connecting them is known as the line of nodes.

This period differs from the sidereal period because both the orbital plane of the object and the plane of the ecliptic precess with respect to the fixed stars, so their intersection, the line of nodes, also precesses with respect to the fixed stars.

Usually, cellular automata are defined with an homogenous topology, i.e. a single line of nodes, a square or hexagonal grid of nodes or an even higher dimensional structure, but each variable (node in the grid) may take on more than two values (and hence not be boolean).

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.