Hodograph

A hodograph is a diagram that gives a vectorial visual representation of the movement of a body or a fluid. It is the locus of one end of a variable vector, with the other end fixed. The position of any plotted data on such a diagram is proportional to the velocity of the moving particle. It is also called a velocity diagram. It appears to have been used by James Bradley, but its practical development is mainly from Sir William Rowan Hamilton, who published an account of it in the "Proceedings of the Royal Irish Academy" in 1846.
Applications.
It is used in physics, astronomy, solid and fluid mechanics to plot deformation of material, motion of planets or any other data that involves the velocities of different parts of a body.
See Swinging Atwood's machine
Meteorology.
In meteorology, hodographs are used to plot winds from soundings of the Earth's atmosphere. It is a polar diagram where wind direction is indicated by the angle from the center axis and its strength by the distance from the center. In the figure to the right, at the bottom one finds values of wind at 4 heights above ground. They are plotted by the vectors formula_1 to formula_2. One has to notice that direction are plotted as mentioned in the upper right corner.
With the hodograph and thermodynamic diagrams like the tephigram, meteorologists can calculate:
Distributed Hodograph.
It is a method of presenting the velocity field of a point in planar motion. The velocity vector, drawn at scale, is shown perpendicular rather than tangent to the point path, usually oriented away from the center of curvature of the path. 
Hodograph transformation.
Hodograph transformation is a technique used to transform nonlinear partial differential equations into linear version. It consists of interchanging the dependent and independent variables in the equation to achieve linearity.