Pursuit curve

Simple pursuit curve

A curve of pursuit is a curve constructed by analogy to having a point or points representing pursuers and pursuees; 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 pursued (leader), for every $t$ with $F'(t) \neq 0$ there is an $x$ such that

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

Single pursuer

Curves of pursuit with different parameters

The path followed by a single pursuer, following a pursuee that moves at constant speed on a line, is a radiodrome. It is a solution of the differential equation $1+ y' ² = k ² (a-x ²) y" ²$ .

Multiple pursuers

Curve of pursuit of vertices of a square (the mice problem for n=4).

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. An example of this is the mice problem.

External links

Wikimedia Commons has media related to Curve of pursuit.

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

Differential transforms of plane curves

Unary operations	Evolute Involute Dual curve Inverse curve Parallel curve Isoptic

Unary operations defined by a point	Pedal & Contrapedal curves Negative pedal curve Pursuit curve Caustic

Unary operations defined by two points	Strophoid

Binary operations defined by a point	Roulette

Operations on a family of curves	Envelope

This article is issued from Wikipedia - version of the 9/20/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.

Pursuit curve

Single pursuer

Multiple pursuers

See also

External links