2. Introduction to Pursuit curves
As bluntly implied by the name, a pursuit curve shows the path/trajectory of an object
takes whenever it is pursuing another object.The velocity vector of the pursuer is
always in the direction of the thing/person being pursued.
One particle travels along a specified curve, while a second pursues it, with
a motion always directed toward the first. The velocities of the two
particles are always in the same ratio.
The question then becomes “When do the two points meet?”
3. Different types of pursuit curves
• Four different categories of pursuit curves generally
I. One dimensional pursuit in a plane with a linear track and uniform speeds
These are the basic pursuit curves where one particle travels in a straight line at some constant velocity and the
pursuing particle changes its trajectory according to the position of the
II. Pursuit curves for a circular track
Curves of pursuit that instead of having a linear tracks the paths of both the pursuer and the object/person being
pursued make circles
III. Pursuit curves for multiple pursuers
These curves have pursuers converging to one point and it generally referred to as the “mice problem
IV. Differential equations valid for arbitrary track and variable speeds
These kinds of curves have changing speeds for the pursuer and object/person being pursued
4. Brief history of pursuit curves
• Some believe that
pursuit curves originated
from Leonardo daVinci
• It was thoroughly investigated
by Pierre Bouguer in 1732 who
was a French scientist
• It wasn’t until George
Boole in his “Treatise of
differential equations” in
1859 that the term
“Pursuit Curve” was
coined for these kind of
curves
5. Category I pursuit curves
• These can be regarded as Basic pursuit curves and are the simplest to solve for
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16. After a long process of multiple slides we are
done and have found our pursuit curve
20. • The circular problem was modeled for a fox and a rabbit but it has multitudes of
applications
• Satellites being launched into orbit
• Sending stuff to the international Space Station (ISS)
• Launching rockets to space
Editor's Notes
Can think of this as phasor for each vector, polar and rectangular forms are related through eulers formula
h(t) is it’s position vector
Dh(t) is it’s velocity vector
Think of as force directed along a line, it represents the velocity in cartesian form in each direction
