释义 |
Arc LengthArc length is defined as the length along a curve,
 | (1) |
Defining the line element , parameterizing the curve in terms of a parameter , and notingthat is simply the magnitude of the Velocity with which the end of the Radius Vector moves gives
 | (2) |
In Polar Coordinates,
 | (3) |
so
In Cartesian Coordinates,
Therefore, if the curve is written
 | (8) |
then
 | (9) |
If the curve is instead written
 | (10) |
then
 | (11) |
Or, in three dimensions,
 | (12) |
so
 | (13) |
See also Curvature, Geodesic, Normal Vector, Radius of Curvature, Radius of Torsion,Speed, Surface Area, Tangential Angle, Tangent Vector, Torsion (Differential Geometry),Velocity |