geodesic

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geodesic

1. relating to or involving the geometry of curved surfaces
2. the shortest line between two points on a curved or plane surface

geodesic

[¦jē·ə¦des·ik]
(mathematics)
A curve joining two points in a Riemannian manifold which has minimum length.

geodesic

geodesic
Great circle is the shortest distance between two points.
The shortest distance between two points on any surface. The shortest distance between two places on earth derived mathematically is called a geodetic line.
References in periodicals archive ?
By solving the scalar geodesic equation for a mass-bearing particle ("stone-like objects"), we shall obtain that the relativistic mass of the object changes according to the remoteness to the observer in the particular space.
As a result, we obtain the scalar geodesic equation, which is the equation of energy of the particle, and the vectorial geodesic equation (the three-dimensional equation of motion).
Here we are interested in the derivation of the generalized geodesic equation of motion such that our geodesic paths correspond to the formal solution of the quantum gravitational wave equation in the preceding section.
Given that a geodesic equation must be produced, for a monochromatic wave, the form of a photonic energy tensor should be similar to that of massive matter.
z]) = 0, formula (6) does produces a geodesic equation if Eq.
We therefore will solve the isotropic geodesic equations in the metric (8).
where we present only those components of Christoffel's symbols which will be used in the geodesic equations (equations of of motion).
We should also add that, coming from the geodesic equation along the z-axis, which is the third equation of (61), to the simplified form (62) thereof, we omitted the harmonic term from consideration.
We show via Einstein's equations and the geodesic equations in a space perturbed by a disc undergoing oscillatory bounces orthogonal to its own plane, that there is no role of superconductivity; the Podkletnov effect is due to the fact that the field of the background space non-holonomity (the basic non-othogonality of time lines to the spatial section), being perturbed by such an oscillating disc produces energy and momentum flow in order to compensate the perturbation in itself.
In terms of physically observable quantities--chronometric invariants (Zelmanov, 1944), which are the respective projections of four-dimensional quantities onto the time line and spatial section of a given observer--the isotropic geodesic equations are presented with two projections onto the time line and spatial section, respectively [1-3]
alpha]] it is necessarily to solve the geodesic equations for free particles (2.
We solve the second problem using the geodesic equations for light-like particles (photons, which are mediators for microwave radiation, and for any electromagnetic radiation in general).