Treatise on Natural Philosophy, Volume 1At the University Press, 1888 - 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 . supposition we have On this 0 = d ( ds2 ) = d ( dx2 + dy3 ) = 2 ( dx d2x + dy d3y ) , where we denote by the suffix to the letter d , the independent variable understood in the ...
... described by a point as the independent variable . supposition we have On this 0 = d ( ds2 ) = d ( dx2 + dy3 ) = 2 ( dx d2x + dy d3y ) , 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 1 γ ( compare § 136 ) . that of The curvature in a circular section being cos3 a sin a cos a the helix is , of course , The tortuosity is or γ до π tan a × curvature . Hence , if a ...
... described on a right circular cylinder of of a curve 1 γ ( compare § 136 ) . that of The curvature in a circular section being cos3 a sin a cos a the helix is , of course , The tortuosity is or γ до π tan a × curvature . Hence , if a ...
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 ...
Contents
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Common terms and phrases
action altered angular velocity anticlastic B₁ Cambridge centre of inertia change of direction circle co-ordinates coefficients component condition configuration constant corresponding curvature curve cycloidal cylinder degrees of freedom Demy 8vo denote diagram differential equation direction cosines distance dt dt dx dy dx² dy dy dy dz edition ellipse ellipsoid elongation equal equations of motion equilibrium expression finite fixed fluid force function geodetic geometrical given gyrostatic Hence infinitely small initial integral kinetic energy length moving P₁ parallel parallelepiped particle perpendicular polygon position principal axes quadratic function quantity radius ratio rectangular 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 theorem tion twist values Y₁ αξ λ² аф
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