Treatise on Natural Philosophy, Volume 1At the University Press, 1888 - Mechanics, Analytic |
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Page xi
... Initial and altered Position of Lines of no Elongation - Simple Shear - Axes of a Shear - Measure of a Shear - Ellipsoidal specification of a Shear - Analysis of a Strain Displacement of a Body , rigid or not , one point of which is ...
... Initial and altered Position of Lines of no Elongation - Simple Shear - Axes of a Shear - Measure of a Shear - Ellipsoidal specification of a Shear - Analysis of a Strain Displacement of a Body , rigid or not , one point of which is ...
Page xiv
... Initial and Final Co - ordinates and the Energy ; its differential Coefficients equal re- spectively to Initial and Final Momentums , and to the time from beginning to end - Same Propositions for Ge- neralized Co - ordinates ...
... Initial and Final Co - ordinates and the Energy ; its differential Coefficients equal re- spectively to Initial and Final Momentums , and to the time from beginning to end - Same Propositions for Ge- neralized Co - ordinates ...
Page 21
... initial and final velocities . This is the case of a stone falling vertically . For if the acceleration be parallel to x , we have d2x di = a , therefore dx dt = v at , and x = { ať3 . dv And we may write the equation ( § 29 ) v dx = a ...
... initial and final velocities . This is the case of a stone falling vertically . For if the acceleration be parallel to x , we have d2x di = a , therefore dx dt = v at , and x = { ať3 . dv And we may write the equation ( § 29 ) v dx = a ...
Page 63
... initial or final position , which were successively made axes of rotation ; and inclined to their plane at an angle equal to half the supplement of the common angle of rotation . A ' A B ' B of rotations tions in one 87. Hence to ...
... initial or final position , which were successively made axes of rotation ; and inclined to their plane at an angle equal to half the supplement of the common angle of rotation . A ' A B ' B of rotations tions in one 87. Hence to ...
Page 76
... initial point , ωγ 1 ds r dt sin ( sin ̄1r + sin ̄1 r ′ ) 1 ds r dt ( r √1 − r22 + r ' √1 – r2 ) , which , as s , r ' and w are known in terms of t , gives r in terms of t , or of s , as we please . Hence , by a single quadrature ...
... initial point , ωγ 1 ds r dt sin ( sin ̄1r + sin ̄1 r ′ ) 1 ds r dt ( r √1 − r22 + r ' √1 – r2 ) , which , as s , r ' and w are known in terms of t , gives r in terms of t , or of s , as we please . Hence , by a single quadrature ...
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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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