Treatise on Natural Philosophy, Part 1University Press, 1886 - Calculators |
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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 ds from one another along the curve , and let do 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 ds from one another along the curve , and let do 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 . when ds is diminished without limit . Let OL , OL ' Let the direction cosines of osity . OL be a , b , c ; OL ' 99 a ' , b ' , c ' ; OQ 99 l , m , n ; OR 99 a , ß , y ; OS 99 λ , μ , ν ...
... angle between OL ' and LO produced through 0 . when ds is diminished without limit . Let OL , OL ' Let the direction cosines of osity . OL be a , b , c ; OL ' 99 a ' , b ' , c ' ; OQ 99 l , m , n ; OR 99 a , ß , y ; OS 99 λ , μ , ν ...
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 ...
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Common terms and phrases
acceleration action altered angular velocity anticlastic application 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 dy dy dy dz 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 Laplace's equation length moving P₁ parallel parallelepiped particle perpendicular polygon position principal axes 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 whole x₁ y₁ αξ λ² аф