Treatise on Natural Philosophy, Volume 1At the University Press, 1888 - Mechanics, Analytic |
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Results 1-5 of 93
Page 1
... angles . If the motion be that of a material particle , however , there cannot generally be any such abrupt changes of ... angle . It is useful to consider at the outset various theorems connected VOL . I. 1 point . Motion of a with the ...
... angles . If the motion be that of a material particle , however , there cannot generally be any such abrupt changes of ... angle . It is useful to consider at the outset various theorems connected VOL . I. 1 point . Motion of a with the ...
Page 2
... angle between the tangents is the change of direction required , and the rate of change is to be measured by the relation between this angle and the length of the circular arc . Let I be the angle , c the arc , and p the radius . We see ...
... angle between the tangents is the change of direction required , and the rate of change is to be measured by the relation between this angle and the length of the circular arc . Let I be the angle , c the arc , and p the radius . We see ...
Page 4
... angle between the tangents at two points at a distance Es 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 ...
... angle between the tangents at two points at a distance Es 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 ...
Page 5
... angle between OL and LO produced through 0 . Let the direction cosines of OS OL be a , b , c c ; OL ' " " a ' , b ' , c ' ; ов 29 l , m , n ; OR " " a , B , y ; OS " " λ , μ , ν : and let 80 denote the angle LOL ' . We have , by the ...
... angle between OL and LO produced through 0 . Let the direction cosines of OS OL be a , b , c c ; OL ' " " a ' , b ' , c ' ; ов 29 l , m , n ; OR " " a , B , y ; OS " " λ , μ , ν : and let 80 denote the angle LOL ' . We have , by the ...
Page 7
... angle through which this turns during the motion of the point exhibits what we have thus defined as the integral curvature . In estimating this , we must of course take the enlarged modern meaning of an angle , including angles greater ...
... angle through which this turns during the motion of the point exhibits what we have thus defined as the integral curvature . In estimating this , we must of course take the enlarged modern meaning of an angle , including angles greater ...
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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