9762

Spherical Harmonic on Constant Latitude or Longitude

View the oscillating radial amplitude of the spherical harmonic (relative to the radial offset of 1.0) on a horizontal plane taken at constant latitude or on a vertical plane taken at constant longitude. You can set the degree and order of the harmonic ({, } with ), the latitude () when the "latitude" button is selected, or the longitude () when the "longitude" button is selected. The relative amplitude (0 to 1) of the harmonic, when added to the constant radial offset of 1.0, is controlled by the slider labeled "scale". Use the "" control to change the oscillation speed, to start or stop it.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

Spherical harmonics (normalized) in the radial direction are expressed by the equation:
,
where and are the degree and order, respectively, of the generalized Legendre function . The function is expressed on a sphere with polar angle (starting from 0 at the positive axis) and azimuth (counterclockwise from the axis in the equatorial plane as viewed from the positive axis).
For display purposes in this Demonstration, is multiplied by the time function , scaled by a constant [0,1] and then added to 1.0. The radial motion in a plane given by constant or is then shown as a function of time, with a complete oscillation every units of time.
There are three common classes of radial spherical harmonics. The first, zonal harmonics of degree , is given when . For this class, there is no longitudinal variation and there are zeros along parallels of latitude. The second, sectoral harmonics of degree and order , has no latitudinal zeros but has zeros along longitudes. The third, tesseral harmonics of degree and order (), has zeros along parallels of latitude and zeros along longitudes.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+