# Abel problem

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To find, in a vertical plane , a curve such that a material point moving along it under gravity from rest, starting from a point with ordinate , will meet the -axis after a time , where the function is given in advance. The problem was posed by N.H. Abel in 1823, and its solution involves one of the first integral equations — the Abel integral equation — which was also solved. In fact, if is the angle formed by the tangent of the curve being sought with the -axis, then Integrating this equation between and and putting one obtains the integral equation for the unknown function , the determination of which makes it possible to find the equation of the curve being sought. The solution of the equation introduced above is: How to Cite This Entry:
Abel problem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Abel_problem&oldid=12327
This article was adapted from an original article by B.V. Khvedelidze (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article