Hodograph

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hodograph

[′häd·ə‚graf]
(physics)
The curve traced out in the course of time by the tip of a vector representing some physical quantity.
In particular, the path traced out by the velocity vector of a given particle.

Hodograph

 

in mechanics, a curve that is a locus of the ends of a variable vector whose values at different moments of time are laid off from a fixed origin O (see Figure 1).

Figure 1. Construction of velocity hodograph

The concept of the hodograph was introduced by the English scientist W. Hamilton. The hodograph visually and geometrically represents the changes with time of a physical quantity, represented by a variable vector, and the rate of this change, which has the same direction as the tangent to the hodograph. For example, the velocity of a point is a quantity represented by the variable vector v. Plotting the values of vector v from the origin O at different moments of time, we derive the velocity hodograph. The quantity characterizing the rate of change in velocity at point M (that is, the acceleration w at point M) for any moment of time has the same direction as the tangent to the velocity hodograph at the corresponding point (M’).

S. M. TARG

References in periodicals archive ?
1, the hodographs of the MF represent strongly elongated ellipses, and at point 1 the coefficient of ellipticity (the ratio of the smaller semiaxis of the ellipse to the larger semiaxis) is generally zero, so that the hodograph of the vector of the MF is stretched into a vertical line.
The layout of the current conductors and the points in which the hodographs of the MP will be considered are shown in Fig.
2, the hodographs of the MF of this PL also represent strongly elongated ellipses, and at point 1 the major axis of the ellipse is in the horizontal plane.
shows the scheme of the arrangement of the current conductors and the points at which the hodographs of the MF will be considered, and Fig.
Caption: Figure 3: Velocity hodographs at points (a) M and (b) N.
3,c shown in the hodograph formed induction vector of the total magnetic field generated by power lines and compensating windings when the active screening system.