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 ?
The circular hodograph represents a 0-3-km storm-relative helicity value of -1,847 [m.sup.2] [s.sup.-2], and the total profile contains 8.3 cm of precipitable water.
Lavicka, "Pythagorean hodograph curves: a survey of recent advances," Journal for Geometry and Graphics, vol.
since Im [??](i[omega]) = - Im [??](i[omega]) for any hodograph [??](i[omega]); [for all][omega] [member of] [R.sub.0+].
Therefore, using such a system, it is possible to compensate for the semimajor axis of the ellipse of the hodograph of the induction vector of the magnetic field and to obtain a sufficiently high screening efficiency for a weakly polarized MF.
Yuan, "A mixed boundary value problem for Chaplygin's hodograph equation," Journal of Mathematical Analysis and Applications, vol.
Further, according to the hypothesis that small streamline deflections produce proportionally small change in Mach number and pressure, a hodograph solution for compressible flow past a corner was given by Verhoffetal.
Among their topics are cooperative path planning and mission planning, designing Dubins paths using analytical geometry, Pythagorean hodograph paths in three dimensions, avoiding mapped and unmapped obstacles, and multiple path planning for simultaneous arrival.
(Naeem, 2003) indicated that Hodograph transformation method can also be used to obtain the exact solutions and obtained some exact solutions.
His thesis on the "Velocity-Correction Factors and the Hodograph Method in Gas Dynamics" later was published by the University of Tehran.
To the degree that the pre-storm environment is known and that convection is going to occur, a forecaster can simply look at the hodograph and determine to a good approximation whether there is sufficient shear over a sufficient depth to promote supercell development (e.g.
From the analysis of the fixed meanings also follows that the compensation process convergence is determined by the position of the hodograph of the transfer function R(j[omega]) = [W.sub.k]'(j[omega])--[W.sub.k](j[omega])F(j[omega]) inside a circumference of a single radius.
The shear strain ([DELTA][gamma]) after one pass through the shear plane (OO') can be determined from the velocity hodograph [9] to derive the following relation: