Chaplygin problem
{{Short description|Solved question in mathematics}}
In mathematics, particularly in the fields of nonlinear dynamics and the calculus of variations, the Chaplygin problem is an isoperimetric problem with a differential constraint. 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 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
- {{cite book|author=Akhiezer, N. I.|author-link=Naum Akhiezer|title=The Calculus of variations|url=https://archive.org/details/calculusofvariat00akhi|url-access=registration|publisher=Blasidel|location=New York|year=1962|pages=[https://archive.org/details/calculusofvariat00akhi/page/206 206–208]|isbn=3-7186-4805-9}}
- {{cite journal|author=Klamkin, M. S.|author-link=Murray S. Klamkin|title=On Extreme length flight paths|journal=SIAM Review|volume=18|issue=2|year=1976|pages=486–488|doi=10.1137/1018079}}
- {{cite journal|author1=Klamkin, M. S. |author2=Newman, D. J.|title=Flying in a wind field I, II|journal=Amer. Math. Monthly|volume=76|pages=16–23, pp. 1013–1019|year=1969|doi=10.2307/2316780|issue=1|publisher=Mathematical Association of America|jstor=2316780}}
See also
- Isoperimetric inequality : zero wind speed case
Category:Calculus of variations
{{mathapplied-stub}}