Treatise on Natural Philosophy, Volume 1, Part 1At the University Press, 1879 - Mechanics, Analytic |
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Page 4
... distance ds from one another along the curve , and let dø be the angle between the osculating planes at these points . Thus , denoting by p the radius of curvature , and the tortuosity , we have 1 P = T = do ds do ds " " according to ...
... distance ds from one another along the curve , and let dø be the angle between the osculating planes at these points . Thus , denoting by p the radius of curvature , and the tortuosity , we have 1 P = T = do ds do ds " " according to ...
Page 9
... distance measured along the line from any one point to any other , remains constant , however the line be bent . 15. The use of a cord in mechanism presents us with many practical applications of this theory , which are in general ex ...
... distance measured along the line from any one point to any other , remains constant , however the line be bent . 15. The use of a cord in mechanism presents us with many practical applications of this theory , which are in general ex ...
Page 20
... distance from that axis , the path is an ellipse or hyperbola whose principal diameters coincide with those axes ; and the acceleration is directed to or from the origin at every instant . dx = dy dt = VX . dt μy , Hence = dx · μνα ...
... distance from that axis , the path is an ellipse or hyperbola whose principal diameters coincide with those axes ; and the acceleration is directed to or from the origin at every instant . dx = dy dt = VX . dt μy , Hence = dx · μνα ...
Page 23
... distance from it , the path is a plane curve , which is the harmonic curve if the acceleration be towards the plane , and a more or less fore - shortened catenary ( § 580 ) if from the plane . As in case c , d2z dt = dz 0 , dt - 0 , and ...
... distance from it , the path is a plane curve , which is the harmonic curve if the acceleration be towards the plane , and a more or less fore - shortened catenary ( § 580 ) if from the plane . As in case c , d2z dt = dz 0 , dt - 0 , and ...
Page 27
... distance . We have obviously duced from Newton's law of force . d2x dt = мос Một dây = m 203 ja , dt2 p2 = x2 + y3 . where dy dx Hence , as in § 36 , x y = dt dt .h ....... . ( 1 ) , See our smaller work , § 51 . Hodograph for planet or ...
... distance . We have obviously duced from Newton's law of force . d2x dt = мос Một dây = m 203 ja , dt2 p2 = x2 + y3 . where dy dx Hence , as in § 36 , x y = dt dt .h ....... . ( 1 ) , See our smaller work , § 51 . Hodograph for planet or ...
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Common terms and phrases
acceleration action algebraic angular velocity anticlastic application Cambridge centre of inertia circle co-ordinates coefficients component configuration constant corresponding course curvature curve cycloidal cylinder degrees of freedom denote determined differential equation direction cosines displacement distance dt dt dt dy dx dy dy dy dy dz dynamical ellipsoid equal equations of motion equilibrium expression finite fluid force formula function give given gyrostatic Hence impulse infinitely small instant integral kinetic energy length linear mass measured momentum moving negative notation osculating plane P₁ parallel particle path perpendicular polygon position principal axes principle quadratic quadratic function quantity radius rectangular resultant rigid body rolling roots rotation round simple harmonic motions solution space spherical harmonic spherical surface St John's College strain suppose tangent plane theorem tion values whole zero αξ
Popular passages
Page 241 - Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it may be compelled by impressed forces to change that state.