	Planetary Systems of the Earth 1 Classic Systems

	Copyright © Klaus Piontzik


German Version

2.11.1 - Angle part

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

Equation 2.11.1.1

These are the spherical harmonics in complex notation.

The Euler equation applies:

e^i·mφ = cos(m·φ) + i·sin(m·φ)

The N_m and P_m 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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