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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).
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’).
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