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.