Feb 16, 2015 · I want to calculate a unit direction vector of a direction with given the azimuth and elevation (cf. http://en.wikipedia.org/wiki/Azimuth), respectively $$\alpha \in [0^{\circ},360^{\circ}), \qquad...

Jun 10, 2012 · It's now fairly easy to calculate the azimuth and elevation of the object. To get the azimuth, just do an atan2 on the x/z coordinates of the object. To get the elevation, project the object coordinates onto the x/z plane (just set the y coordinate to 0), then do: acos(dot(normalise(object coordinates), normalise(projected coordinates)))

The horizontal coordinate system is a celestial coordinate system that uses the observer's local horizon as the fundamental plane to define two angles of a spherical coordinate system: altitude and azimuth.

Although ⃗e and ⃗h represent 6 components, we only actually need three. The ⃗h represents orientation of the orbital plane, and so we don’t care about the roll axis in the classic 1-2-3 rotation matrices. That is, this orientation has symmetry about the angular momentum vector.

Explain how the magnitude of a vector is defined in terms of the components of a vector. Identify the direction angle of a vector in a plane. Explain the connection between polar coordinates and Cartesian coordinates in a plane.

Mx, My, and Mz are the scalar components of the external moments vector. These are often known as Euler’s Equations of Motion. Note the difficulties that arise with equations (19) and (21) when = ± /2. Where [TBP] is a transformation matrix from the body to the planet coordinate system and the vehicle-carried planet coordinate system.

Vector quantities have magnitude and direction. Represented by an arrow. In 2D require two numbers to specify (e.g. azimuth and length, x and y coordinates) In 3D require 3 numbers (eg plunge trend and length, x, y and z coordinates) Sometimes it's useful to …

Planetographic coordinates are applicable only to bodies that have a reference spheroid and a spin direction. Coordinates are longitude, latitude, and altitude. longitude is the planetographic longitude of the point (or vector head, with the vector tail at the origin).

Altitude is the angular distance of an object above the local horizon. It ranges from 0 degrees at the horizon to 90 degrees at the zenith, the spot directly overhead. Azimuth is the angular distance of an object from the local North, measured along the horizon.

For each angle pair (e.g., azimuth and elevation angles), a figure is given which shows the two angles, the coordinate system to which they are referred, and unit vectors in the directions of increases in the two angles. The unit vector in the direction of increasing elevation angle is used in calculating the refraction