Treatise on Natural Philosophy, Part 1University Press, 1886 - Calculators |
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Page 18
... proportional to the square of the velocity and also to the curvature of the path . The former of these changes the velocity , the other affects only the form of the path , or the direction of motion . Hence if a moving point be subject ...
... proportional to the square of the velocity and also to the curvature of the path . The former of these changes the velocity , the other affects only the form of the path , or the direction of motion . Hence if a moving point be subject ...
Page 20
... proportional to its distance from that axis , the path is an ellipse or hyperbola whose principal diameters coincide with those axes ; and the acceleration is directed to or from the origin at every instant . dx dt - Hence d2x dt2 d'y ...
... proportional to its distance from that axis , the path is an ellipse or hyperbola whose principal diameters coincide with those axes ; and the acceleration is directed to or from the origin at every instant . dx dt - Hence d2x dt2 d'y ...
Page 21
... proportional to the squares of the times tion . elapsed since the commencement of the motion . In this case the space described in any interval is that which would be described in the same time by a point moving uniformly with a ...
... proportional to the squares of the times tion . elapsed since the commencement of the motion . In this case the space described in any interval is that which would be described in the same time by a point moving uniformly with a ...
Page 23
... proportional to the distance from it , the path is a plane curve , which is the harmonic curve if the acceleration be towards the plane , and a more or less fore - shortened catenary ( § 580 ) if from the plane . As in case C , dez dt ...
... proportional to the distance from it , the path is a plane curve , which is the harmonic curve if the acceleration be towards the plane , and a more or less fore - shortened catenary ( § 580 ) if from the plane . As in case C , dez dt ...
Page 24
... proportional to the times . Also , the area actually described in any instant depends on the length of the radius - vector and the velocity perpendicular to it , and is shown below to be unaffected by an acceleration parallel to the ...
... proportional to the times . Also , the area actually described in any instant depends on the length of the radius - vector and the velocity perpendicular to it , and is shown below to be unaffected by an acceleration parallel to the ...
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Common terms and phrases
acceleration action altered angular velocity anticlastic application 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 dy dy dy dz 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 Laplace's equation length moving P₁ parallel parallelepiped particle perpendicular polygon position principal axes 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 whole x₁ y₁ αξ λ² аф