Pursuit curve

Curves of pursuit with different parameters

A curve of pursuit is a curve constructed by analogy to having a point or points which represents pursuers and pursuees, and the curve of pursuit is the curve traced by the pursuers.

With the paths of the pursuer and pursuee parameterized in time, the pursuee is always on the pursuer's tangent. That is, given F(t) the pursuer (follower) and L(t) the pursuee (leader), there is for every t with F′(t) ≠ 0 an x such that

$L(t)=F(t)+xF^\prime(t). \,$

Multiple pursuers

Curve of pursuit of vertices of a square

Typical drawings of curves of pursuit have each point acting as both pursuer and pursuee, inside a polygon, and having each pursuer pursue the adjacent point on the polygon.

See also

• Logarithmic spiral
• Tractrix

External links

• Mathworld, with a slightly narrower definition that |L′(t)| and |F′(t)| are constant

This geometry-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Curves Geometry stubs Wikimedia Foundation. 2010. Игры ⚽ Нужна курсовая? N-curve Curve sketching Look at other dictionaries: pursuit curve — noun : the interception curve made by an interceptor maintaining continuous fire on a moving airplane from a position to the rear and side compare lead collision course …   Useful english dictionary Curve of pursuit — Pursuit Pur*suit , n. [F. poursuite, fr. poursuivre. See {Pursue}, v. t.] 1. The act of following or going after; esp., a following with haste, either for sport or in hostility; chase; prosecution; as, the pursuit of game; the pursuit of an enemy …   The Collaborative International Dictionary of English Pursuit — Pur*suit , n. [F. poursuite, fr. poursuivre. See {Pursue}, v. t.] 1. The act of following or going after; esp., a following with haste, either for sport or in hostility; chase; prosecution; as, the pursuit of game; the pursuit of an enemy.… …   The Collaborative International Dictionary of English Curve of pursuit — A curve of pursuit is a curve constructed by analogy to having a point or points which represents pursuers and pursuees, and the curve of pursuit is the curve traced by the pursuers. With the paths of the pursuer and pursuee parametrised in time …   Wikipedia curve of pursuit — persekiojimo trajektorija statusas T sritis Gynyba apibrėžtis Trajektorija, kuria naikintuvas skrenda atakuodamas judantį taikinį ir išlaikydamas reikiamą taikymo kryptį. atitikmenys: angl. curve of pursuit pranc. courbe de poursuite …   NATO terminų aiškinamasis žodynas curve of pursuit — The curved path followed by an attacker onto target aircraft when attacking from a position that is not directly astern, or straight ahead, and while holding the proper aiming allowance. Ideally, an aircraft should be line astern of the target at …   Aviation dictionary curve of pursuit — a curve described by a point moving always directly toward or from a second point that is itself moving according to some law …   Useful english dictionary curve of pursuit — The curved path described by a fighter plane making an attack on a moving target while holding the proper aiming allowance …   Military dictionary Crash Time: Autobahn Pursuit — Developer(s) Synetic …   Wikipedia List of curve topics — This is a list of curve topics in mathematics. See also curve, list of curves, and list of differential geometry topics.*acnode *algebraic curve *arc *asymptote *asymptotic curve *Barbier s theorem *barycentric… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”