Treatise on Natural Philosophy, Volume 1, Part 1At the University Press, 1879 - Mechanics, Analytic |
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Page 2
... described by a moving point , and these we shall now take up , deferring the considera- tion of Velocity to a future section , as being more closely con- nected with physical ideas . Curvature of a plane curve . 4. The direction of ...
... described by a moving point , and these we shall now take up , deferring the considera- tion of Velocity to a future section , as being more closely con- nected with physical ideas . Curvature of a plane curve . 4. The direction of ...
Page 3
... described by a point as the independent variable . On this supposition we have 0 = d ( ds2 ) = d ( dx2 + dy3 ) = 2 ( dx d ̧3x + dy d ̧3y ) , where we denote by the suffix to the letter d , the independent variable understood in the ...
... described by a point as the independent variable . On this supposition we have 0 = d ( ds2 ) = d ( dx2 + dy3 ) = 2 ( dx d ̧3x + dy d ̧3y ) , where we denote by the suffix to the letter d , the independent variable understood in the ...
Page 8
... described in the preceding section . Thus the tortuosity may be measured by the help of the spherical curve which we have just used for defining integral curvature . We cannot as yet complete the explanation , as it depends on the ...
... described in the preceding section . Thus the tortuosity may be measured by the help of the spherical curve which we have just used for defining integral curvature . We cannot as yet complete the explanation , as it depends on the ...
Page 9
... described on a right circular cylinder of of a curve ( compare 1 § 136 ) . curvature radius r . The curvature in a circular section being that of cos2 a sin a cos a the helix is , of course , The tortuosity is or g π tan ax curvature ...
... described on a right circular cylinder of of a curve ( compare 1 § 136 ) . curvature radius r . The curvature in a circular section being that of cos2 a sin a cos a the helix is , of course , The tortuosity is or g π tan ax curvature ...
Page 10
... described by the help of its analogous focal property ; and so on . 17. But the consideration of evolutes is of some importance in Natural Philosophy , especially in certain dynamical and optical questions , and we shall therefore ...
... described by the help of its analogous focal property ; and so on . 17. But the consideration of evolutes is of some importance in Natural Philosophy , especially in certain dynamical and optical questions , and we shall therefore ...
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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.