Term for pertaining to the polar direction

Question

I am discussing a system (in a scientific context) which is described with spherical polar coordinates. This has a radial coordinate r, a polar angle θ and a azimuth angle φ. A diagram can be found on the linked page.

I would like a term to describe (for example) motion in the polar direction (increasing or decreasing θ). The equivalent terms for the other two directions would be "radial" and "azimuthal". There are several possibilities:

• "Polar" is the obvious choice, but this could also mean motion of the pole itself.

• "Poloidal" seems to mean the correct thing, but might only refer to a toroidal, instead of a spherical, geometry.

• "Poleward", but this has connotations of only being towards the nearest pole. Hence the word we are looking for is to "poleward" as "vertical" is to "upward".

• "Vertical" is used by some, as the θ direction is parallel to the z-axis in the equatorial plane, and the z-axis is commonly taken to be the vertical direction. However, this is inappropriate close to the pole when the θ direction becomes horizontal.

• "Latitudinal" describes the correct direction, but seems odd when not paired with "longitudinal" for azimuthal motion.

Is there another term, or is there a clear best option?

Answer 1

Conventionally, motion toward the pole in spherical coordinates is poleward. (Or, stated another way, any motion that results in a change of the polar angle is toward one pole or the other, and is thus poleward.)

You'll also find polewards used, but poleward is preferred about 10:1 in the literature.

Answer 2

I'm thinking in terms of Azimuths, which are classified into (3) types:

1) True North: A line from any point on the earth's surface to the north pole. All lines of longitude are true north lines. True north is usually represented by a star on most topographical or contour maps' declination diagram.

2) Magnetic North (magnetic azimuth): The direction to the north magnetic pole, as indicated by the north-seeking needle of a magnetic instrument. Magnetic north is usually symbolized by a line ending with half of an arrowhead. Magnetic readings are obtained using a magnetic compass, such as a lensatic compass or a M2 compass.

3) Grid North (grid azimuth): The north that is established by using the vertical grid lines on the map. Grid north may be symbolized by the letters GN or the letter "y".

Answer 3

Have you considered resorting to cardinal directions? Re-reading your question, I cannot tell whether you are referring to north-south motion or east-west, but if you picked one, I would instantly know what you meant.