Elements of Natural Philosophy |
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Page 11
... axis , the path is an ellipse or hyperbola whose principal diameters coincide with those axes ; and the acceleration is directed to or from the centre of the curve at every instant ( S $ 66 , 78 ) . ( c ) If the components of the ...
... axis , the path is an ellipse or hyperbola whose principal diameters coincide with those axes ; and the acceleration is directed to or from the centre of the curve at every instant ( S $ 66 , 78 ) . ( c ) If the components of the ...
Page 46
... principal axes of a strain are the principal axes of the ellipsoid into which it converts a sphere . The principal elongations of a strain are the elongations in the direction of its principal axes . 145. When the positions of the principal ...
... principal axes of a strain are the principal axes of the ellipsoid into which it converts a sphere . The principal elongations of a strain are the elongations in the direction of its principal axes . 145. When the positions of the principal ...
Page 47
... principal axes are equal , that is to say , in a circle . Hence the elongations along all lines in either of these planes are equal to the elongation along the mean principal axis of the strain ellipsoid . 148. The consideration of the ...
... principal axes are equal , that is to say , in a circle . Hence the elongations along all lines in either of these planes are equal to the elongation along the mean principal axis of the strain ellipsoid . 148. The consideration of the ...
Page 48
... principal axes of a shear are the lines of maximum elongation and of maximum contraction respectively . They may be ... principal axis of elongation , and the latter is the principal axis of contraction , in their initial positions . The ...
... principal axes of a shear are the lines of maximum elongation and of maximum contraction respectively . They may be ... principal axis of elongation , and the latter is the principal axis of contraction , in their initial positions . The ...
Page 49
... principal axes . 153. The ratio of a shear is the ratio of elongation and contrac- tion of its principal axes . Thus if one principal axis is elongated in the ratio : a , and the other therefore ( § 148 ) contracted in the ratio a : 1 ...
... principal axes . 153. The ratio of a shear is the ratio of elongation and contrac- tion of its principal axes . Thus if one principal axis is elongated in the ratio : a , and the other therefore ( § 148 ) contracted in the ratio a : 1 ...
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Common terms and phrases
acceleration action amount angular velocity anticlastic attraction axis called centimetre centre of gravity centre of inertia circle circular co-ordinates component configuration consider constant corresponding cosine couple curvature curve cylinder denote density described diagram displacement distance ellipse ellipsoid elongation equal equations equilibrium external point finite fixed point flexure fluid forces acting formulae friction geometrical given force Hence hodograph horizontal inclined infinitely small instant inversely kinetic energy length magnitude mass matter measured moment of inertia momentum moving normal section P₁ parallel parallelogram particle path pendulum perpendicular plane perpendicular portion position pressure principal axes principle produce projection proportional quantity radius radius of gyration reckoned rectangular relative right angles rigid body rotation round shear shell sides simple harmonic motion solid angle space spherical surface spiral square straight line strain stress suppose tangent theorem tion torsion uniform unit vertical vibrations weight whole wire