Chaplygin Problem
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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. The airplane is assumed to be constrained to move in a plane, moving at a constant airspeed v, and the wind is assumed to move in a const...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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. The airplane is assumed to be constrained to move in a plane, moving at a constant airspeed v, 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 eccentricity is w/v.
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