Treatise on Natural Philosophy, Volume 1, Part 1At the University Press, 1879 - Mechanics, Analytic |
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Page 3
... dy 0 = tan - 1 ; dx and , by differentiation with reference to any independent variable t , we have de . = Also , dy d dx dx d'y - dy d'x ( dy dx2 + dy3 1 + ds = ( dx2 + dy3 ) 3 . Hence , if p denote the radius of curvature , so that 1 ...
... dy 0 = tan - 1 ; dx and , by differentiation with reference to any independent variable t , we have de . = Also , dy d dx dx d'y - dy d'x ( dy dx2 + dy3 1 + ds = ( dx2 + dy3 ) 3 . Hence , if p denote the radius of curvature , so that 1 ...
Page 5
... dy ds dz " dx a ' ds bc'b'c = ds ' dy a - a - d - b - d , cod ( 8 ) ; ds ' dydz dz , dy - d ds ds dsds 9 n = ; ds dz c'c = d ... ( 8 ) ; ds & c . . ( 9 ) ; Curvature and tortu- osity . and a , ẞ , 9. ] 5 KINEMATICS .
... dy ds dz " dx a ' ds bc'b'c = ds ' dy a - a - d - b - d , cod ( 8 ) ; ds ' dydz dz , dy - d ds ds dsds 9 n = ; ds dz c'c = d ... ( 8 ) ; ds & c . . ( 9 ) ; Curvature and tortu- osity . and a , ẞ , 9. ] 5 KINEMATICS .
Page 6
... dy d dy dx d ds ds ds ds μ = " ν ρ ds pds ( 11 ) . dy , dz dz , dy d d - ds ds ds ds p - ' ds - ds ds ds ds The simplest expression for the curvature , with choice of inde- pendent variable left arbitrary , is the following , taken ...
... dy d dy dx d ds ds ds ds μ = " ν ρ ds pds ( 11 ) . dy , dz dz , dy d d - ds ds ds ds p - ' ds - ds ds ds ds The simplest expression for the curvature , with choice of inde- pendent variable left arbitrary , is the following , taken ...
Page 14
... dy dz we have u = " dt v = dt ' w = Hence , calling a , ß , y the dt • angles which the direction of motion makes with the axes , and ds putting q = we have dt ' dx dx dt и COS α = = ds ds Չ dt Hence u = = q cos a , and therefore 26. A ...
... dy dz we have u = " dt v = dt ' w = Hence , calling a , ß , y the dt • angles which the direction of motion makes with the axes , and ds putting q = we have dt ' dx dx dt и COS α = = ds ds Չ dt Hence u = = q cos a , and therefore 26. A ...
Page 16
... dy dt ' dt dt dr do sin + cos 0 dt dx dy But by 26 the whole velocity along r is cos + sin 0 , dt dt dr dt i.e. , by the above values , Similarly the transverse velocity is • Accelera- tion . dy dt dx do cos - sin 0 , or r dt dt 28. The ...
... dy dt ' dt dt dr do sin + cos 0 dt dx dy But by 26 the whole velocity along r is cos + sin 0 , dt dt dr dt i.e. , by the above values , Similarly the transverse velocity is • Accelera- tion . dy dt dx do cos - sin 0 , or r dt dt 28. The ...
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acceleration action algebraic altered angular velocity anticlastic application axis Cambridge centre of inertia circle co-ordinates coefficients component condition configuration constant corresponding course curvature curve cycloidal cylinder denote determined differential equation direction cosines displacement distance dt dt dx dy dy dy dy dz ellipsoid elongation equal equations of motion equilibrium expression finite fixed force formula function geometrical given gyrostatic harmonic motions Hence impulse infinitely small instant integral kinetic energy length linear momentum moving negative osculating plane P₁ parallel particle perpendicular polygon position principal axes quadratic quadratic function quantity radius ratio rectangular resultant right angles rigid body rolling roots rotation round shear simple harmonic simple harmonic motions solution spherical harmonic spherical surface St John's College strain suppose tangent plane theorem tion values whole Y₁ λ² аф
Popular passages
Page 241 - Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it may be compelled by impressed forces to change that state.