For instance, in the case of the parabola, the distance of any particle from the directrix is equal to its distance from the focus.
"The Romance of Mathematics" by P. Hampson
But General Thomas's plan turned on cavalry work as its directrix.
"Was General Thomas Slow at Nashville?" by Henry V. Boynton
The only surface of revolution having this property is the catenoid formed by the revolution of a catenary about its directrix.
"Encyclopaedia Britannica, 11th Edition, Volume 5, Slice 3" by Various
Thus AB is the directrix of the parabola VED, of which F is the focus.
"The New Gresham Encyclopedia" by Various
Similarly, in an hyperbola a vertex is nearer to the directrix than to the focus.
"Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6" by Various
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We proceed with the technical issue of recovering directrix from coordinates and momenta of strings pieces at a given time t0 in a way which can be used in numerical simulations.
On asimuthal anisotropy in fragmentation of classical relativistic string
Upon integrating (13) and taking into account that y(t0) = x(t0 , σ = 0) is a position of one of the string’s ends, one recovers the directrix on the interval t ∈ (t0 − σmax , t0 + σmax ), and, hence, at any point due to its periodicity.
On asimuthal anisotropy in fragmentation of classical relativistic string
To illustrate the technique described in the previous section, we reconstruct directrix for two simple model initial conditions.
On asimuthal anisotropy in fragmentation of classical relativistic string
To recover directrix we’ll start with drawing a tra jectory of the upper endpoint of the string for (0, σmax) time interval, that is using ﬁrst line of (14).
On asimuthal anisotropy in fragmentation of classical relativistic string
For σ ∈ (p/κ , p/κ + b), we have only the second one of the two differentials in the directrix increment (14) which goes against x2 .
On asimuthal anisotropy in fragmentation of classical relativistic string
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