# 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

Macmillan and Company, 1871 - 278 pages
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### Contents

 CHAPTER I 1 CHAPTER II 13 CHAPTER III 32 CHAPTER IV 54 CHAPTER V 68 CHAPTER VI 100 CHAPTER VII 126
 CHAPTER VIII 147 CHAPTER X 196 CHAPTER XI 220 CHAPTER XII 243 CHAPTER XIII 250 CHAPTER XIV 259

### Popular passages

Page 163 - 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 262 - 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 156 - 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 156 - ... 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 247 - Let 6 be the angle which the tangent to the curve makes with the ^ axis.
Page 134 - 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...
Page 27 - Now x — - is the abscissa of the point of intersection of the tangent to the curve at the point (x, y) and the axis of x ; we will put f for this abscissa.
Page 76 - If p be the radius of curvature at any point of the concave portion we have .y=y Thus at the points P and Q since the curve touches the straight lines we have 22/! + £. = 2/t. 3a p a