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 altered angular velocity anticlastic application Cambridge centre of inertia change of direction circle co-ordinates coefficients component condition configuration constant corresponding course curvature curve cycloidal cylinder degrees of freedom denote determined diagram differential equation direction cosines distance dt dt dx dy dy dz ellipse ellipsoid elongation equal equations of motion equilibrium expression finite fixed fluid force function geometrical given gyrostatic Hence infinitely small initial instant integral kinetic energy length linear ment momentum moving parallel parallelepiped particle perpendicular polygon position principal axes quantity radius ratio rectangular resultant right angles rigid body rolling roots rotation round shear simple harmonic simple harmonic motions simple shear solution spherical harmonic spherical surface strain suppose synclastic tangent plane tangential displacement theorem tion twist values whole αξ λ²
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.