In
mathematics, particularly in the fields of
nonlinear dynamics and the
calculus of variations
The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions
and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...
, the Chaplygin problem is an isoperimetric problem with a
differential constraint
Constraint may refer to:
* Constraint (computer-aided design), a demarcation of geometrical characteristics between two or more entities or solid modeling bodies
* Constraint (mathematics), a condition of an optimization problem that the solution ...
. Specifically, the problem is to determine what flight path an airplane in a constant wind field should take in order to encircle the maximum possible area in a given amount of time. The airplane is assumed to be constrained to move in a plane, moving at a constant
airspeed
In aviation, airspeed is the speed of an aircraft relative to the air. Among the common conventions for qualifying airspeed are:
* Indicated airspeed ("IAS"), what is read on an airspeed gauge connected to a Pitot-static system;
* Calib ...
''v'', for time ''T'', and the wind is assumed to move in a constant direction with speed ''w''.
The solution of the problem is that the airplane should travel in an
ellipse whose major axis is perpendicular to ''w'', with eccentricity ''w''/''v''.
References
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Calculus of variations
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