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 & be the angle between the osculating planes at these points . Thus , denoting by p the radius of curvature , and the tortuosity , we have T 1 P = do ds do T = ds 80 Curvature and ...
... distance ds from one another along the curve , and let & be the angle between the osculating planes at these points . Thus , denoting by p the radius of curvature , and the tortuosity , we have T 1 P = do ds do T = ds 80 Curvature and ...
Page 9
... distance r from the fixed straight line , the axis of the cylinder ) , will have finite curvature 1 tortuosity , being - tan a or P 1 ( 1-9 ) . √ pr P The will in the limit be a mean proportional between the curvature of the circular ...
... distance r from the fixed straight line , the axis of the cylinder ) , will have finite curvature 1 tortuosity , being - tan a or P 1 ( 1-9 ) . √ pr P The will in the limit be a mean proportional between the curvature of the circular ...
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 dt = 1 , dy dt = VX . Hence · = μνχ , dx dt ...
... 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 dt = 1 , dy dt = VX . Hence · = μνχ , dx dt ...
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 , perpendicular to at any ...
... 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 , perpendicular to at any ...
Page 27
... distance . We have obviously d2x μα dt = " d3y_py Jo dt2 y2 = x2 + y3 . = duced from Newton's law of force . where dy dx Hence , as in § 36 , x y = h .... dt dt * See our smaller work , § 51 . . ( 1 ) , Hodograph for planet or comet ...
... distance . We have obviously d2x μα dt = " d3y_py Jo dt2 y2 = x2 + y3 . = duced from Newton's law of force . where dy dx Hence , as in § 36 , x y = h .... dt dt * See our smaller work , § 51 . . ( 1 ) , Hodograph for planet or comet ...
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Common terms and phrases
acceleration action algebraic altered angular velocity anticlastic application axis Cambridge centre of inertia circle co-ordinates coefficients component condition configuration constant corresponding course curvature curve cycloidal cylinder denote determined differential equation direction cosines displacement distance dt dt dx dy dy dy dy dz ellipsoid elongation equal equations of motion equilibrium expression finite fixed force formula function geometrical given gyrostatic harmonic motions Hence impulse infinitely small instant integral kinetic energy length linear momentum moving negative osculating plane P₁ parallel particle perpendicular polygon position principal axes quadratic quadratic function quantity radius ratio rectangular resultant right angles rigid body rolling roots rotation round shear simple harmonic simple harmonic motions solution spherical harmonic spherical surface St John's College strain suppose tangent plane theorem tion values whole Y₁ λ² аф
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.