Treatise on Natural Philosophy, Volume 1, Issue 1University Press, 1879 - 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 88 from one another along the curve , and let 84 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 88 from one another along the curve , and let 84 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 OL be a , b , c ; OL ' 99 a ' , b ' , c ' ; 0Q 1 , m , n ; 99 OR " 9 a , B , y ; OS 99 λ , μ , ν : and let 80 denote the angle LOL ' . We have , by the elements ...
... angle between OL and LO produced through 0 . Let the direction cosines of OL be a , b , c ; OL ' 99 a ' , b ' , c ' ; 0Q 1 , m , n ; 99 OR " 9 a , B , y ; OS 99 λ , μ , ν : and let 80 denote the angle LOL ' . We have , by the elements ...
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 algebraic angular velocity anticlastic application arbitrary axis Cambridge centre of inertia circle co-ordinates coefficients component configuration constant corresponding course curvature curve cycloidal cylinder denote determined differential equation direction cosines displacement distance dt dt dt dy dx dy dy dy dy dz ellipsoid equal equations of motion equilibrium expression finite fixed force formula function give given gyrostatic harmonic motions Hence impulse infinitely small instant integral kinetic energy Lagrange's linear mass measured momentum moving negative 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 simple harmonic motions solution spherical harmonic spherical surface St John's College strain suppose tangent plane theorem tion values variable whole Y₁ αξ λ² аф
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