Treatise on Natural Philosophy, Volume 1, Issue 1University Press, 1879 - Calculators |
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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 dt = a , therefore dx dt = v = at , and x = at3 . dv And we may write the equation ( § 29 ) v = = α ...
... initial and final velocities . This is the case of ' a stone falling vertically . For if the acceleration be parallel to x , we have d2x dt = a , therefore dx dt = v = at , and x = at3 . dv And we may write the equation ( § 29 ) v = = α ...
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 . Α ' 41 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 . Α ' 41 B ' B of rotations tions in one 87. Hence to ...
Page 76
... initial point , wr ' : = 1 ds rdt sin ( sin1r + sin1 ' ) = 1 ds r dt 12 -2 ( r √ 1 − y'2 + r ' √ 1 — r2 ) , which , as 8 , r ' and ∞ are known in terms of t , gives r in terms of t , or of s , as we please . Hence , by a single ...
... initial point , wr ' : = 1 ds rdt sin ( sin1r + sin1 ' ) = 1 ds r dt 12 -2 ( r √ 1 − y'2 + r ' √ 1 — r2 ) , which , as 8 , r ' and ∞ are known in terms of t , gives r in terms of t , or of s , as we please . Hence , by a single ...
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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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