hodograph

American  

[hod-uh-graf, -grahf] / ˈhɒd əˌgræf, -ˌgrɑf /

noun

Mathematics, Mechanics.

1. the figure described by the extremity of a vector that has a fixed origin and a position vector equal to the velocity of a moving particle.

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hodograph British  

/ ˈhɒdəˌɡrɑːf, -ɡræf /

noun

1. a curve of which the radius vector represents the velocity of a moving particle

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Other Word Forms

• hodographic adjective

Etymology

Origin of hodograph

1840–50; < Greek hod ( ós ) way + -o- + -graph

Example Sentences

This method is indeed indicated at § 37, but no diagram is given, and the properties of the hodograph are investigated by means of Cartesians.

From Project Gutenberg

From this definition we have the following important fundamental property which belongs to all hodographs, viz. that at any point the tangent to the hodograph is parallel to the direction, and the velocity in the hodograph equal to the magnitude of the resultant acceleration at the corresponding point of the orbit.

From Project Gutenberg

This will be evident if we consider that, since radii vectores of the hodograph represent velocities in the orbit, the elementary arc between two consecutive radii vectores of the hodograph represents the velocity which must be compounded with the velocity of the moving point at the beginning of any short interval of time to get the velocity at the end of that interval, that is to say, represents the change of velocity for that interval.

From Project Gutenberg

Hence the elementary arc divided by the element of time is the rate of change of velocity of the moving-point, or in other words, the velocity in the hodograph is the acceleration in the orbit.

From Project Gutenberg

Every orbit must clearly have a hodograph, and, conversely, every hodograph a corresponding orbit; and, theoretically speaking, it is possible to deduce the one from the other, having given the other circumstances of the motion.

From Project Gutenberg