Hodograph
of a vector field along a curve
The curve representing the ends of the variable vector (
is a real variable, such as time) whose origin for all
is a given fixed point
. Trajectory of a point Velocity hodograph Construction of a velocity hodograph.
Figure: h047500a
The hodograph is a visual geometrical representation of the variation (with ) of the magnitude represented by the variable vector and of the rate of this change. Its direction is that of the tangent to the hodograph. For example, if the velocity of a moving point is represented by a variable vector
, then by drawing the values of
at different moments of time from the origin
, one obtains the velocity hodograph. The magnitude describing the rate of the variation of the velocity at some point
, i.e. the acceleration
at that point, has at any point of time the direction of the tangent to the velocity hodograph at the respective point.
Hodograph. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Hodograph&oldid=15147