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 1871Macmillan and Company, 1871 - 278 pages |
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Common terms and phrases
1+p² 1+p³ axis of revolution axis of x boundary C₁ C₂ Calculus of Variations catenary circle circular arc condition continuous solution convex corresponding cos² cos³ cusp cycloid dc₁ denote diagram discontinuous solution dp)² dx dx dx dy dx² dy dp dy dx ellipse expression fixed points given curve given length given points given volume greater Hence horizontal imposed infinitesimal integral sign investigation Jacobi's method least value less limits maximum or minimum moment of inertia negative obtain ordinate P₁ p²)² parabola pass path portion problem quickest descent radius of curvature required curve Required the curve resistance satisfied second order shew sin² sin³ solid of revolution Sp)² straight line suppose surface Sy dx tangent term Todhunter's touch vanish velocity Y₁ zero аф
Popular passages
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...