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.

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.

See also

  • Visual calculus, a related approach useful in solving a variety of integral calculus problems.
  • Laplace–Runge–Lenz vector, for an example in solving the Kepler problem

References

Further reading

  • Hamilton, William Rowan. "The Hodograph, or a New Method of Expressing in Symbolic Language the Newtonian Law of Attraction", Proceedings of the Royal Irish Academy, Vol. 3 (1847), pp. 344–353. Edited by David R. Wilkins (2000).
  • In his book Matter and Motion, Maxwell writes: and he applies these techniques to analyse Kepler's first and second laws. Free "Matter and Motion" e-books are available on the Internet.
  • Feynman's Lost Lecture: The Motion of Planets Around the Sun by David Goodstein & Judith R. Goodstein (, W. W. Norton & Company: New York, 1996). In this book the hodograph is used to geometrically derive elliptical (Keplerian) orbits from Newton's laws of motion and gravitation.
  • The Hodograph - Dr. James B. Calvert, University of Denver