PiMath.de Planetary Systems of the Earth 1
Classic Systems
 
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2.11.1 - Angle part

Following general solution function is specified for the part of the angle:
 
Equation 2.11.1.1 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..


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 Planetare Systeme 1

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Der Autor - Klaus Piontzik