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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?

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    If by motion in the polar direction you mean 'motion toward a polar point', then polewards is what you want. If you mean 'motion in either direction along an axis called the polar axis', then there's no obvious candidate; but you could call it polar axial movement, or make up a compound like polaxial.
    – John Lawler
    Aug 5, 2013 at 16:29
  • Thanks for the suggestion. I do mean something like your former suggestion, but I'm hoping for a general term that could be used for motion either towards or away from the pole. I think polewards is explicitly towards the pole and not away from it (towards the equator), hence it does not quite fit.
    – CPLB
    Aug 5, 2013 at 17:37
  • It's a sphere. If you move in a direction that changes the polar angle, you're moving toward one pole or the other.
    – Gnawme
    Aug 5, 2013 at 18:21
  • @Gnawme technically correct (the best form of correct), but I don't think that is intuitive. If you were on an expedition across Antarctica and just gone past the south pole, would you say you were heading polewards since you are now moving due north?
    – CPLB
    Aug 6, 2013 at 11:56

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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.

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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". enter image description here

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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.

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  • I am referring to what would be north-south motion. However, I shall be dealing with systems which are not the Earth and so do not have a real north or south.
    – CPLB
    Aug 6, 2013 at 11:52
  • You have to have an "up" pole and a "down" pole, or the sign won't make any sense. Up is north. (Screw you, Australia!)
    – Michael Lorton
    Aug 6, 2013 at 16:30

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