PiMath.de Planetary Systems of the Earth 1
Classic Systems
  Copyright © Klaus Piontzik  
 German version    
German Version    

2.11.1 - Angle part

Following general solution function is specified for the part of the angle:
Equation Solution function

These are the spherical harmonics in complex notation.

The Euler equation applies: eimφ = cos(mφ) + isin(mφ)

The Nm and Pm are the so called Legendre polynomials, which can be manipulated like constants in our consideration.

So results total:

Solution function

Multiplying the clips it is found:

Solution function

And here you can see again the multiplicative associated sine and cosine functions, so tesseral spherical harmonics or grids. Here equipped with a real and an imaginary part, so a complex function as a general solution for the angle part of the Laplace's equation..

 to previous page back home next  next page


 Planetare Systeme 1

buy on Amazon

200 sides, 23 of them in color
154 pictures
38 tables

Production und Publishing:
Books on Demand GmbH, Norderstedt

ISBN 978-3-7357-3854-7

Price: 25 Euro



Der Autor - Klaus Piontzik