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 general who advances without coveting fame and retreats without fearing disgrace, whose only thought is to protect his country and do good service for his sovereign, is the jewel of the kingdom.”
—Sun Tzu (6th–5th century B.C.)
“What he loved so much in the plant morphological structure of the tree was that given a fixed mathematical basis, the final evolution was so incalculable.”
—D.H. (David Herbert)
“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)