Results 1 to 8 of 8

Math Help - Spherical Vector To Cartesian Vector

  1. #1
    Newbie
    Joined
    Jul 2010
    Posts
    16

    Spherical Vector To Cartesian Vector

    Hello everyone,

    I have a quick and straightforward problem, that I need some help with.

    Suppose I have a spherical vector defined by a radius and two angles, denoted by <rho,theta,psi>. Where, rho is the radius, theta is an angle, and so is psi.

    Which that being said, how would I convert that spherical vector into a Cartesian vector.

    (Note: I know how to convert from Spherical to Cartesian;
    x=rho*sin(psi) *cos(theta)
    Y=rho*sin(psi) *sin(theta)
    Z=rho*cos(theta)

    Would these conversion also be appropriate if the input is a spherical vector, and the required output is a Cartesian vector.

    Thanks for the help.
    Taylor S. Amarel
    Learning is living
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2009
    Posts
    806
    Thanks
    4
    theta is an angle, and so is psi.

    with respect to what? Which one is the reference line?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2010
    Posts
    16
    Theta= The angle of rotation around Y on the XZ plane
    Psi= The angle of rotation around Z on the YX plane

    So the reference direction would be X? Is that right, if I knew the formula I am sure I could swap variables out into their proper location for my coordinate system
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Your equations to convert from spherical to cartesian are incorrect. The x and y must have sin(theta) in them, where theta is the polar angle (measured down from the positive z axis), and z must have cos(theta) in it. What changes in x and y is the trig function of the azimuthal angle (measured around the z axis).
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jul 2010
    Posts
    16
    So if I understand you correctly, the conversion would be as follows.
    x=rho*sin(theta)*cos(psi)
    y=rho*sin(theta)*sin(psi)
    z=rho*cos(theta)
    I am correct?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    That is correct. Does this solve your problem?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Jul 2010
    Posts
    16

    Thank You!

    Quote Originally Posted by Ackbeet View Post
    That is correct. Does this solve your problem?
    Yes, indeed it does. Kudos for the help, and have a good day.

    Thanks,
    Taylor S. Amarel
    Learning is Living
    Follow Math Help Forum on Facebook and Google+

  8. #8
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    You're welcome. Have a good one!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Vector spherical harmonics
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: April 27th 2011, 09:56 AM
  2. Normal vector of spherical curve
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: January 26th 2010, 08:46 PM
  3. Vector parametric and cartesian form
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: January 24th 2010, 04:44 PM
  4. Vector Calculus in Spherical Polar Co-ords.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 26th 2008, 09:18 AM
  5. Replies: 3
    Last Post: September 1st 2008, 03:21 AM

Search Tags


/mathhelpforum @mathhelpforum