Researches in the Calculus of Variations, Principally on the Theory of Discontinuous Solutions: An Essay to which the Adams Prize was Awarded in the University of Cambridge in 1871

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Macmillan and Company, 1871 - 278 pages
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Page 266 - An important remark must be made with respect to relative maxima and minima which, so far as I know, is not to be found in treatises on the subject.
Page 189 - Is there any stationary solution for the brachistochrone when angular points are allowed ? 2. To find the form of a solid which experiences a minimum resistance when it moves through a fluid in the direction of the axis of revolution (Todhunter, Researches p.
Page 160 - A particle is projected from a given point with a given velocity and is acted on by a given force to a fixed point.
Page 160 - ... a fixed point by a force varying inversely as the square of the distance : determine the path of minimum action to a second fixed point.
Page 251 - Let 6 be the angle which the tangent to the curve makes with the ^ axis.
Page 138 - Prove that an arc of a circle from the lowest point which does not exceed 60° is a curve of quicker descent than any other curve which can be drawn within the same arc; and...

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