Treatise on Natural Philosophy, Volume 1At the University Press, 1888 - Mechanics, Analytic |
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Page vii
... remarkable functions known as Laplace's Co- efficients . There can be but one opinion as to the beauty and utility of this analysis of Laplace ; but the manner in which it has been hitherto presented has seemed repulsive to the ablest ...
... remarkable functions known as Laplace's Co- efficients . There can be but one opinion as to the beauty and utility of this analysis of Laplace ; but the manner in which it has been hitherto presented has seemed repulsive to the ablest ...
Page 26
... remarkable theorems to which it led him is that of § 38 . Since the radius - vector of the hodograph represents the velocity at each instant , it is evident ( § 27 ) that an elementary arc represents the velocity which must be ...
... remarkable theorems to which it led him is that of § 38 . Since the radius - vector of the hodograph represents the velocity at each instant , it is evident ( § 27 ) that an elementary arc represents the velocity which must be ...
Page 133
... remarkable corollary that three pure strains produced one after another , in any piece of matter , each without rotation , may be so adjusted as to leave the body unstrained , but rotated through some angle about some axis . We shall ...
... remarkable corollary that three pure strains produced one after another , in any piece of matter , each without rotation , may be so adjusted as to leave the body unstrained , but rotated through some angle about some axis . We shall ...
Page 142
... remarkable proposition , and its converse , that if F ( x , y , z ) denote any function of the co - ordinates of any point of a body , and if every such point be displaced from its given position ( x , y , z ) to the point whose co ...
... remarkable proposition , and its converse , that if F ( x , y , z ) denote any function of the co - ordinates of any point of a body , and if every such point be displaced from its given position ( x , y , z ) to the point whose co ...
Page 144
... remarkable that ssas { 1 ( dy _ds ) dz + m da dy ) + n ( 1/8 dz dx da ) } dx dy is the same for all surfaces having common curvilinear boundary ; and when a , ß , y are the components of a displacement from x , y , z , it is the entire ...
... remarkable that ssas { 1 ( dy _ds ) dz + m da dy ) + n ( 1/8 dz dx da ) } dx dy is the same for all surfaces having common curvilinear boundary ; and when a , ß , y are the components of a displacement from x , y , z , it is the entire ...
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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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