Treatise on Natural Philosophy, Volume 1, Issue 1University Press, 1879 - Calculators |
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Page 9
... proportional between the curvature of the circular section of the cylinder and the finite curvature of the curve . The acceleration ( or force ) required to produce such a motion of a point ( or material particle ) will be afterwards ...
... proportional between the curvature of the circular section of the cylinder and the finite curvature of the curve . The acceleration ( or force ) required to produce such a motion of a point ( or material particle ) will be afterwards ...
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 . da dt = = μy , Hence d'x ...
... 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 . da dt = = μy , Hence d'x ...
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 ...
... 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 ...
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Common terms and phrases
acceleration action algebraic angular velocity anticlastic application arbitrary axis Cambridge centre of inertia circle co-ordinates coefficients component configuration constant corresponding course curvature curve cycloidal cylinder denote determined differential equation direction cosines displacement distance dt dt dt dy dx dy dy dy dy dz ellipsoid equal equations of motion equilibrium expression finite fixed force formula function give given gyrostatic harmonic motions Hence impulse infinitely small instant integral kinetic energy Lagrange's linear mass measured momentum moving negative P₁ parallel particle path perpendicular polygon position principal axes principle quadratic quadratic function quantity radius rectangular resultant rigid body rolling roots rotation round simple harmonic simple harmonic motions solution spherical harmonic spherical surface St John's College strain suppose tangent plane theorem tion values variable whole Y₁ αξ λ² аф
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