Spherical Harmonic on Constant Latitude or Longitude
 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.   "Spherical Harmonic on Constant Latitude or Longitude" from The Wolfram Demonstrations Project http://demonstrations.wolfram.com/SphericalHarmonicOnConstantLatitudeOrLongitude/ Contributed by: David von Seggern (University of Nevada) | ||||||||||||||
  
|
Browse all topics
