Treatise on Natural Philosophy, Volume 1At the University Press, 1888 - Mechanics, Analytic |
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Page vi
... corresponding divisions of Dynamics are thus conveniently entitled Statics and Kinetics . One object which we have constantly kept in view is the grand principle of the Conservation of Energy . According to modern experimental results ...
... corresponding divisions of Dynamics are thus conveniently entitled Statics and Kinetics . One object which we have constantly kept in view is the grand principle of the Conservation of Energy . According to modern experimental results ...
Page 4
... corresponding property is conveniently called Tortuosity . 8. The nature of this will be best understood by consider- ing the curve as a polygon whose sides are indefinitely small . Any two consecutive sides , of course , lie in a plane ...
... corresponding property is conveniently called Tortuosity . 8. The nature of this will be best understood by consider- ing the curve as a polygon whose sides are indefinitely small . Any two consecutive sides , of course , lie in a plane ...
Page 6
... corresponding to that of OZ relatively to OX and OY . Then , using ( 8 ) and ( 9 ) , with ( 7 ) , in ( 5 ) and ( 6 ) respectively , we have dx d dy dz d d ds ds ds α p - 1 ds ' B p1 ds γ p - 1 ds .... ( 10 ) ; dy , dz dz , dy dz , dx dx ...
... corresponding to that of OZ relatively to OX and OY . Then , using ( 8 ) and ( 9 ) , with ( 7 ) , in ( 5 ) and ( 6 ) respectively , we have dx d dy dz d d ds ds ds α p - 1 ds ' B p1 ds γ p - 1 ds .... ( 10 ) ; dy , dz dz , dy dz , dx dx ...
Page 26
... corresponding interval of time , to find the velocity at its end . Hence the velocity in the hodo- graph is equal to the acceleration in the path ; and the tangent to the hodograph is parallel to the direction of the acceleration in the ...
... corresponding interval of time , to find the velocity at its end . Hence the velocity in the hodo- graph is equal to the acceleration in the path ; and the tangent to the hodograph is parallel to the direction of the acceleration in the ...
Page 28
... corresponding arc of the hodograph . From this it is easy to see , for example , that if a comet move in a parabola , the amount of heat it receives from the sun in any interval is pro- portional to the angle through which its direction ...
... corresponding arc of the hodograph . From this it is easy to see , for example , that if a comet move in a parabola , the amount of heat it receives from the sun in any interval is pro- portional to the angle through which its direction ...
Contents
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318 | |
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250 | |
361 | |
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384 | |
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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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