Ad
related to: spherical harmonic properties definition geometry examples liststudy.com has been visited by 100K+ users in the past month
Search results
Results From The WOW.Com Content Network
The table of spherical harmonics contains a list of common spherical harmonics. Since the spherical harmonics form a complete set of orthogonal functions and thus an orthonormal basis , every function defined on the surface of a sphere can be written as a sum of these spherical harmonics.
This is a table of orthonormalized spherical harmonics that employ the Condon-Shortley phase up to degree =. Some of these formulas are expressed in terms of the Cartesian expansion of the spherical harmonics into polynomials in x , y , z , and r .
The descriptor "harmonic" in the name harmonic function originates from a point on a taut string which is undergoing harmonic motion.The solution to the differential equation for this type of motion can be written in terms of sines and cosines, functions which are thus referred to as harmonics.
The functions , (,) are the spherical harmonics, and the quantity in the square root is a normalizing factor. Recalling the relation between the associated Legendre functions of positive and negative m, it is easily shown that the spherical harmonics satisfy the identity [5]
Shape descriptors can be classified by their invariance with respect to the transformations allowed in the associated shape definition. Many descriptors are invariant with respect to congruency, meaning that congruent shapes (shapes that could be translated, rotated and mirrored) will have the same descriptor (for example moment or spherical harmonic based descriptors or Procrustes analysis ...
An important geometry related to that of the sphere is that of the real projective plane; it is obtained by identifying antipodal points (pairs of opposite points) on the sphere. Locally, the projective plane has all the properties of spherical geometry, but it has different global properties.
For premium support please call: 800-290-4726 more ways to reach us
The potential V(R) at a point R outside the charge distribution, i.e. | R | > r max, can be expanded by the Laplace expansion: = | | = = = () = (), where () is an irregular solid harmonic (defined below as a spherical harmonic function divided by +) and () is a regular solid harmonic (a spherical harmonic times r ℓ). We define the spherical ...