“geodesic polar coordinates”的概念、定义、翻译、参考文献-科学参考

geodesic polar coordinates

Mathematics

When polar coordinates (r,θ‎) are used to parameterize the plane, centred on the origin, then the first fundamental form is

$d s^{2} = d r^{2} + r^{2} d θ^{2} .$

More generally, at a point on a surface, there is a unique locally defined geodesic in each given tangent direction. Using geodesic polars, so that coordinates (r,θ‎) are assigned to the point distance r along the geodesic in direction θ‎, the first fundamental form has E = 1, F = 0, as above.

单词	geodesic polar coordinates
释义	geodesic polar coordinates Mathematics When polar coordinates (r,θ‎) are used to parameterize the plane, centred on the origin, then the first fundamental form is $d s^{2} = d r^{2} + r^{2} d θ^{2} .$ More generally, at a point on a surface, there is a unique locally defined geodesic in each given tangent direction. Using geodesic polars, so that coordinates (r,θ‎) are assigned to the point distance r along the geodesic in direction θ‎, the first fundamental form has E = 1, F = 0, as above.
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