In a sphere placed in an arbitrary non-stationary flow field of viscous incompressible fluid for stick boundary conditions where the force density s calculations leads to show the generalization of Faxen's theorem to force multipole moments of arbitrary order.
22.
The basic idea is to decompose the particles into groups; particles within a group interact normally ( i . e ., by the full potential ), whereas the energies and forces between groups of particles are calculated from their multipole moments.
23.
The electrostatic interaction model of ions in solids has thus been extended to a point multipole concept that also includes higher multipole moments like dipoles, quadrupoles etc . These concepts require the determination of higher order Madelung constants or so-called electrostatic lattice constants.
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The creator of the theory of general relativity, Albert Einstein, argued in 1916 that gravitational radiation should be produced, according to his theory, by any mass-energy configuration that has a time-varying quadrupole moment ( or higher multipole moment ).
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In the first ( more common ) case, the coefficients of the series expansion are called " exterior multipole moments " or simply " multipole moments " whereas, in the second case, they are called " interior multipole moments ".
26.
In the first ( more common ) case, the coefficients of the series expansion are called " exterior multipole moments " or simply " multipole moments " whereas, in the second case, they are called " interior multipole moments ".
27.
In the first ( more common ) case, the coefficients of the series expansion are called " exterior multipole moments " or simply " multipole moments " whereas, in the second case, they are called " interior multipole moments ".
28.
In weak field general relativity, it is convenient to treat isolated sources using another type of multipole, which generalize the Weyl moments to " mass multipole moments " and " momentum multipole moments ", characterizing respectively the distribution of mass and of momentum of the source.
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In weak field general relativity, it is convenient to treat isolated sources using another type of multipole, which generalize the Weyl moments to " mass multipole moments " and " momentum multipole moments ", characterizing respectively the distribution of mass and of momentum of the source.
30.
This is usually informally stated as follows : " any inhomogeneities in the spacetime geometry outside a black hole will be radiated away " . ( Any such inhomogeneities can be quantified as nonzero higher multipole moments . ) Price's theorem explains how the no hair theorem is enforced.
