- Source: Pursuit curve
In geometry, 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) ≠ 0 there is an x such that
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{\displaystyle L(t)=F(t)+xF'\!(t).}
History
The pursuit curve was first studied by Pierre Bouguer in 1732. In an article on navigation, Bouguer defined a curve of pursuit to explore the way in which one ship might maneuver while pursuing another.
Leonardo da Vinci has occasionally been credited with first exploring curves of pursuit. However Paul J. Nahin, having traced such accounts as far back as the late 19th century, indicates that these anecdotes are unfounded.
Single pursuer
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
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.
See also
Logarithmic spiral
Tractrix
Circles of Apollonius#Apollonius pursuit problem
Pursuit–evasion
References
External links
Mathworld, with a slightly narrower definition that |L′(t)| and |F′(t)| are constant
MacTutor Pursuit curve
Kata Kunci Pencarian:
- Jan and Dean
- Pursuit curve
- List of curves
- Basic fighter maneuvers
- Gallery of curves
- List of curves topics
- List of mathematical shapes
- Radiodrome
- The Man in the Moone
- Pursuit–evasion
- Air combat manoeuvring
