|Copyright © Klaus Piontzik
construction of the spatial oscillation structure a
mathematical and physical model is available that allows
to explain the structures of the earth on a basis
The question is:
What is a
general approach for an oscillation structure?
(Marquis de) Laplace (28.03.1749 bis 05.03.1827)
was a French mathematician, physicist, and astronomer. He
worked in the fields of probability theory and
The Laplace operator Nabla is a mathematical operator that is a general mathematical provision (calculation way). The Laplace operator is a differential vector operator within the multidimensional analysis.
The Laplace operator occurs in Laplace's equation, for example. Twice continuously differentiable solutions of this equation are called harmonic functions.
|to be read: Nabla f is zero
Expressed in cartesian coordinates (x, y, z):
Applies in only one dimension:
the equation for a harmonic oscillator,
such as a pendulum or a spring without friction.
The Laplace's equation represents a mathematical formula to describe oscillation phenomena in space.
The common approach to a solution with a central configuration is to transform the Cartesian coordinates (x, y, z) in spherical coordinates (lambda, phi, r).
Then, the entire function is decomposed into two part functions. Where a function the radial part contains and the other function the part of the angle.
The general approach to a solution function of Laplace's equation in spherical coordinates looks like this:
part functions R and Y can be solved in
each case individually.
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