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IEVref: | 102-04-22 | ID: | |

Language: | en | Status: Standard | |

Term: | abscissa, <along a curve> | ||

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Definition: | for a given point of an oriented curve with an origin point, real number, the absolute value of which is the length of the curve between the origin and the given point, and the sign is positive or negative depending on whether the path from the origin to the given point is consistent or not with the orientation of the curve Note 1 to entry: For a curve defined by the position vector $r=f(u)$ as a function of the parameter Note 2 to entry: In the usual geometrical space, the abscissa along a curve is a quantity of the dimension length. | ||

Publication date: | 2008-08 | ||

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Internal notes: | 2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO | ||

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Note 1 to entry: For a curve defined by the position vector $r=f(u)$ as a function of the parameter *u*, with an origin O corresponding to $u=0$, the abscissa of the point M corresponding to *u* = *u*_{M} is the line integral $\underset{\text{O}}{\overset{\text{M}}{\int}}\left|\mathrm{d}r\right|}={\displaystyle \underset{\text{0}}{\overset{{u}_{\text{M}}}{\int}}\left|\frac{\mathrm{d}f}{\mathrm{d}u}\right|\mathrm{d}u$.

Note 2 to entry: In the usual geometrical space, the abscissa along a curve is a quantity of the dimension length.