Definition:Hodograph

Definition

A hodograph is a curve used to work out the acceleration of a point $P$ moving at a known velocity along a curved trajectory.

The hodograph is constructed by drawing (straight) line segments representing vectors $\vec {OH}$ and $\vec {OH'}$ from a reference point $O$ whose length and direction represent the velocity of $P$ at successive positions of $P$ at times $t$ and $t + \delta t$.

The vector $\vec {HH'}$ then represents the change in velocity during the time interval $\delta t$.

Hence the mean acceleration over $\delta t$ is given by:

$\hat {\mathbf a} = \dfrac {\vec {HH'} } {\delta t}$

Hence if $\delta t \to 0$, the velocity of $H$ represents in magnitude and direction the acceleration of $P$.

Also see

• Results about hodographs can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): hodograph
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): hodograph