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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. These 12 ...
Once the radius is fixed, the three coordinates (r, θ, φ), known as a 3-tuple, provide a coordinate system on a sphere, typically called the spherical polar coordinates. The plane passing through the origin and perpendicular to the polar axis (where the polar angle is a right angle) is called the reference plane (sometimes fundamental plane).
Argand diagram refers to a geometric plot of complex numbers as points z = x + iy using the horizontal x-axis as the real axis and the vertical y-axis as the imaginary axis. [3] Such plots are named after Jean-Robert Argand (1768–1822), although they were first described by Norwegian–Danish land surveyor and mathematician Caspar Wessel ...
One example is shown in the diagram, where the rotation takes place about the z-axis. The plane of rotation is the xy-plane, so everything in that plane it kept in the plane by the rotation. This could be described by a matrix like the following, with the rotation being through an angle θ (about the axis or in the plane):
The stereographic projection of a trace is an arc. The Wulff net is arcs corresponding to planes that share a common axis in the (x,y) plane. If the pole and the trace of a plane are represented on the same diagram, then we turn the Wulff net so the trace corresponds to an arc of the net;
y b axis - perpendicular to the x b,z b-plane, positive determined by the right-hand rule (generally, positive out the right wing) Wind frame Origin - airplane center of gravity; x w axis - positive in the direction of the velocity vector of the aircraft relative to the air; z w axis - perpendicular to the x w axis, in the plane of symmetry of ...
The z-axis is vertical and the x-axis is highlighted in green. Thus, the red plane shows the points with x = 1, the blue plane shows the points with z = 1, and the yellow plane shows the points with y = −1. The three surfaces intersect at the point P (shown as a black sphere) with the Cartesian coordinates (1, −1, 1).
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