Adjacent Words

Spherical harmonic analysis definitions

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Webster's 1913 Dictionary

Spherical Spher"ic*al, Spheric Spher"ic, a. [L. sphaericus, Gr. ???: cf. F. sph['e]rique.] 1. Having the form of a sphere; like a sphere; globular; orbicular; as, a spherical body. 2. Of or pertaining to a sphere. 3. Of or pertaining to the heavenly orbs, or to the sphere or spheres in which, according to ancient astronomy and astrology, they were set. Knaves, thieves, and treachers by spherical predominance. --Shak. Though the stars were suns, and overburned Their spheric limitations. --Mrs. Browning. Spherical angle, Spherical co["o]rdinate, Spherical excess, etc. See under Angle, Coordinate, etc. Spherical geometry, that branch of geometry which treats of spherical magnitudes; the doctrine of the sphere, especially of the circles described on its surface. Spherical harmonic analysis. See under Harmonic, a. Spherical lune,portion of the surface of a sphere included between two great semicircles having a common diameter. Spherical opening, the magnitude of a solid angle. It is measured by the portion within the solid angle of the surface of any sphere whose center is the angular point. Spherical polygon,portion of the surface of a sphere bounded by the arcs of three or more great circles. Spherical projection, the projection of the circles of the sphere upon a plane. See Projection. Spherical sector. See under Sector. Spherical segment, the segment of a sphere. See under Segment. Spherical triangle,re on the surface of a sphere, bounded by the arcs of three great circles which intersect each other. Spherical trigonometry. See Trigonometry. -- Spher"ic*al*ly, adv. -- Spher"ic*al*ness, n.

Webster's 1913 Dictionary

the motion of the point A, of the foot of the perpendicular PA, when P moves uniformly in the circumference of a circle, and PA is drawn perpendicularly upon a fixed diameter of the circle. This is simple harmonic motion. The combinations, in any way, of two more simple harmonic motions, make other kinds of harmonic motion. The motion of the pendulum bob of a clock is approximately simple harmonic motion. Harmonic proportion. See under Proportion. Harmonic series or progression. See under Progression. Spherical harmonic analysis, a mathematical method, sometimes referred to as that of Laplace's Coefficients, which has for its object the expression of an arbitrary, periodic function of two independent variables, in the proper form for a large class of physical problems, involving arbitrary data, over a spherical surface, and the deduction of solutions for every point of space. The functions employed in this method are called spherical harmonic functions. --Thomson & Tait. Harmonic suture (Anat.), an articulation by simple apposition of comparatively smooth surfaces or edges, as between the two superior maxillary bones in man; -- called also harmonic, and harmony. Harmonic triad (Mus.), the chord of a note with its third and fifth; the common chord.