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.[1] 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 and fluid mechanics to plot deformation of material, motion of planet or any other data that involves the velocities of different part of a body.

See Swinging Atwood's machine

Meteorology

Hodograph plot of upper air winds from radiosonde (Source: NOAA)

In meteorology, hodographs are used to plot winds from surrounding 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 to . 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:

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.[2]

Further reading

The study of the hodograph, as a method of investigating the motion of a body, was introduced by Sir W. R. Hamilton. The hodograph may be defined as the path traced out by the extremity of a vector which continually represents, in direction and magnitude, the velocity of a moving body. In applying the method of the hodograph to a planet, the orbit of which is in one plane, we shall find it convenient to suppose the hodograph turned round its origin through a right angle, so that the vector of the hodograph is perpendicular instead of parallel to the velocity it represents.
and he applies these techniques to analyse Kepler's first and second laws.
Free "Matter and Motion" e-books are available on the Internet.

See also

References

Further reading

External links

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