Treatise on Natural Philosophy, Volume 1At the University Press, 1888 - Mechanics, Analytic |
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Page 4
... passes from one position to the next by revolving about the tangent to the curve . 9. Thus , as we proceed along such a curve , the curvature in general varies ; and , at the same time , the plane in which the curvature lies is turning ...
... passes from one position to the next by revolving about the tangent to the curve . 9. Thus , as we proceed along such a curve , the curvature in general varies ; and , at the same time , the plane in which the curvature lies is turning ...
Page 7
... passing round the figure . This is true whether the polygon be closed or not . If closed , then , as long as it is not crossed , this sum is four right angles , an extension of the result in Euclid , where all re - entrant polygons are ...
... passing round the figure . This is true whether the polygon be closed or not . If closed , then , as long as it is not crossed , this sum is four right angles , an extension of the result in Euclid , where all re - entrant polygons are ...
Page 23
... passing fixed centre . through that point ; and in this plane the areas traced out by the radius - vector are proportional to the times employed . This includes the case of a satellite or planet revolving about its primary . Evidently ...
... passing fixed centre . through that point ; and in this plane the areas traced out by the radius - vector are proportional to the times employed . This includes the case of a satellite or planet revolving about its primary . Evidently ...
Page 27
... passes through it if a parabola , and the origin is without the hodograph if the orbit is a hyperbola . For a projectile unresisted by the air , it will be shewn in Kinetics that we have the equations ( assumed in § 35 , c ) d2y d2x dt2 ...
... passes through it if a parabola , and the origin is without the hodograph if the orbit is a hyperbola . For a projectile unresisted by the air , it will be shewn in Kinetics that we have the equations ( assumed in § 35 , c ) d2y d2x dt2 ...
Page 30
... passes through Q , the instan- taneous position of the first point . It will be evident , on a moment's consideration , that ... passing through the fixed point , the angle which the joining line makes with a fixed line in the plane is ...
... passes through Q , the instan- taneous position of the first point . It will be evident , on a moment's consideration , that ... passing through the fixed point , the angle which the joining line makes with a fixed line in the plane is ...
Contents
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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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