1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

4D angular coordinate system and corresponding hypervolume element

  1. Mar 4, 2009 #1
    I am looking for a 4D angular coordinate system (radius and three angles) and its corresponding "hypervolume element".

    2D: polar coordinates - dA = r dr dtheta
    3D: spherical coordinates - dV = r^2 sin(phi) dphi dtheta dr
    4D: ?
     
  2. jcsd
  3. Mar 4, 2009 #2
    4-D spherical coordinates:

    x1 = r sin(theta1) sin(theta2) cos(phi)
    x2 = r sin(theta1) sin(theta2) sin(phi)
    x3 = r sin(theta1) cos(theta2)
    x4 = r cos(theta1)

    from which you can compute the hypervolume element.
     
  4. Mar 4, 2009 #3
    Thanks.

    Is "4-D spherical coordinates" established terminology?
    Is this the "standard" transformation? I guess there are other ones?
     
  5. Mar 4, 2009 #4
    I just checked wikipedia. There, the generalization to arbitrary dimension is called http://en.wikipedia.org/wiki/Hypersphere#Hyperspherical_coordinates". They are the same that I gave you in the 4-D case except for the order of the coordinates.
    I don't know what the standard term in the case n=4 is.
     
    Last edited by a moderator: Apr 24, 2017
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: 4D angular coordinate system and corresponding hypervolume element
  1. Coordinate system (Replies: 3)

Loading...