“geodesic”的概念、定义、翻译、参考文献-科学参考

geodesic

Physics

The shortest distance between two points on a curved surface.

Mathematics

A curve on a surface, joining two given points, that is the shortest curve between the two points. On a sphere, a geodesic is an arc of a great circle through the two given points.

For a curve γ‎(s), parameterized by arc length s, this is equivalent to the acceleration vector $\ddot{γ} (s)$ being normal to the surface. A curve γ‎(s) = r(u(s),v(s)) in a parameterized surface r(u,v) is a geodesic if it satisfies the equations

$\frac{d}{d s} (E \dot{u} + F \dot{v}) = \frac{1}{2} (E_{u} {\dot{u}}^{2} + 2 F_{u} \dot{u} \dot{v} + G_{u} {\dot{v}}^{2}),$

$\frac{d}{d s} (F \dot{u} + G \dot{v}) = \frac{1}{2} (E_{v} {\dot{u}}^{2} + 2 F_{v} \dot{u} \dot{v} + G_{v} {\dot{v}}^{2}),$

where E,2F,G are the coefficients of the first fundamental form. See also Christoffel symbols.

Astronomy

The shortest distance in space between two points. On a plane surface a geodesic is a straight line; on a sphere it is part of a great circle. The term is usually used in the context of general relativity, where it represents the shortest route between two points in curved spacetime.

Computer

See reachability.

单词	geodesic
释义	geodesic Physics The shortest distance between two points on a curved surface. Mathematics A curve on a surface, joining two given points, that is the shortest curve between the two points. On a sphere, a geodesic is an arc of a great circle through the two given points. For a curve γ‎(s), parameterized by arc length s, this is equivalent to the acceleration vector $\ddot{γ} (s)$ being normal to the surface. A curve γ‎(s) = r(u(s),v(s)) in a parameterized surface r(u,v) is a geodesic if it satisfies the equations $\frac{d}{d s} (E \dot{u} + F \dot{v}) = \frac{1}{2} (E_{u} {\dot{u}}^{2} + 2 F_{u} \dot{u} \dot{v} + G_{u} {\dot{v}}^{2}),$ $\frac{d}{d s} (F \dot{u} + G \dot{v}) = \frac{1}{2} (E_{v} {\dot{u}}^{2} + 2 F_{v} \dot{u} \dot{v} + G_{v} {\dot{v}}^{2}),$ where E,2F,G are the coefficients of the first fundamental form. See also Christoffel symbols. Astronomy The shortest distance in space between two points. On a plane surface a geodesic is a straight line; on a sphere it is part of a great circle. The term is usually used in the context of general relativity, where it represents the shortest route between two points in curved spacetime. Computer See reachability.
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