Riemann ellipsoid
E468356
astrophysical fluid configuration
ellipsoidal equilibrium configuration
equilibrium figure
rotating fluid body
self-gravitating fluid mass
A Riemann ellipsoid is a rotating, self-gravitating fluid mass in ellipsoidal equilibrium whose internal motion and figure are analyzed in Riemann’s extension of classical ellipsoidal models in celestial mechanics.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
astrophysical fluid configuration
ⓘ
ellipsoidal equilibrium configuration ⓘ equilibrium figure ⓘ rotating fluid body ⓘ self-gravitating fluid mass ⓘ |
| analyzedUsing | ellipsoidal harmonics and tensor methods ⓘ |
| appearsIn | theory of dynamical stability of rotating fluids ⓘ |
| assumes |
Newtonian gravity in the standard formulation
ⓘ
ideal (non-viscous) fluid in the classical treatment ⓘ |
| definedBy | Riemann’s extension of Dirichlet’s ellipsoidal figures ⓘ |
| definedIn | 19th-century work of Bernhard Riemann on rotating fluid masses ⓘ |
| equilibriumCondition |
balance of self-gravity, pressure, and inertial forces
ⓘ
ellipsoidal surfaces of constant density and pressure ⓘ |
| extends |
classical ellipsoidal models of rotating masses
ⓘ
theory of equilibrium figures of rotating fluids ⓘ |
| generalizes |
Jacobi ellipsoid
NERFINISHED
ⓘ
Maclaurin spheroid NERFINISHED ⓘ |
| hasComponent |
centrifugal forces due to rotation
ⓘ
pressure gradients in the fluid ⓘ self-gravity ⓘ |
| hasInternalMotion |
linear velocity field in spatial coordinates
ⓘ
uniform vorticity in the fluid interior (in Riemann’s construction) ⓘ |
| hasParameter |
angular velocity of figure rotation
ⓘ
internal vorticity or circulation parameter ⓘ mass density ⓘ three principal semi-axes of the ellipsoid ⓘ total mass ⓘ |
| hasProperty |
ellipsoidal figure maintained in time
ⓘ
internal fluid motion ⓘ rotating ⓘ self-gravitating ⓘ stationary in a rotating frame ⓘ time-independent shape in equilibrium ⓘ uniform density (in the classical model) ⓘ |
| hasShape |
ellipsoid
ⓘ
triaxial ellipsoid ⓘ |
| namedAfter | Bernhard Riemann NERFINISHED ⓘ |
| relatedTo |
Dirichlet ellipsoids
NERFINISHED
ⓘ
Poincaré’s theory of rotating fluid masses NERFINISHED ⓘ equilibrium figures of rotating homogeneous masses ⓘ |
| satisfies |
Euler equations for an incompressible rotating fluid (in the classical idealization)
ⓘ
Poisson equation for the gravitational potential ⓘ |
| studiedIn |
astrophysical fluid dynamics
ⓘ
celestial mechanics ⓘ gravitational theory of rotating bodies ⓘ |
| usedAsModelFor |
idealized galactic cores
ⓘ
rotating gaseous planets ⓘ rotating stars ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.