General Mathematical Properties
Mathematically, multipole expansions are related to the underlying rotational symmetry of the physical laws and their associated differential equations. Even though the source terms (such as the masses, charges, or currents) may not be symmetrical, one can expand them in terms of irreducible representations of the rotational symmetry group, which leads to spherical harmonics and related sets of orthogonal functions. One uses the technique of separation of variables to extract the corresponding solutions for the radial dependencies.
Read more about this topic: Multipole Expansion
Famous quotes containing the words general, mathematical and/or properties:
“The tremendous outflow of intellectuals that formed such a prominent part of the general exodus from Soviet Russia in the first years of the Bolshevist Revolution seems today like the wanderings of some mythical tribe whose bird-signs and moon-signs I now retrieve from the desert dust.”
—Vladimir Nabokov (1899–1977)
“The most distinct and beautiful statement of any truth must take at last the mathematical form.”
—Henry David Thoreau (1817–1862)
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)