Treatise on Natural Philosophy, Volume 1, Part 1At the University Press, 1879 - Mechanics, Analytic |
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Page 7
... preceding formulæ . Curvature and tortu- osity . curvature ( compare 10. The integral curvature , or whole change of direction of Integral an arc of a plane curve , is the angle through which the tangent of a curve has turned as we pass ...
... preceding formulæ . Curvature and tortu- osity . curvature ( compare 10. The integral curvature , or whole change of direction of Integral an arc of a plane curve , is the angle through which the tangent of a curve has turned as we pass ...
Page 8
... preceding section . Thus the tortuosity may be measured by the help of the spherical curve which we have just used for defining integral curvature . We cannot as yet complete the explanation , as it depends on the theory of rolling ...
... preceding section . Thus the tortuosity may be measured by the help of the spherical curve which we have just used for defining integral curvature . We cannot as yet complete the explanation , as it depends on the theory of rolling ...
Page 13
... preceding definition of velocity is equally applica- Resolution ble whether the point move in a straight or curved line ; but , since in the latter case the direction of motion continually changes , the mere amount of the velocity is ...
... preceding definition of velocity is equally applica- Resolution ble whether the point move in a straight or curved line ; but , since in the latter case the direction of motion continually changes , the mere amount of the velocity is ...
Page 37
... preceding rules . 51. The following practical methods of effecting such a com- bination in the simple case of the movements of two points are useful in scientific illustrations and in certain mechanical arrange- ments . Let two moving ...
... preceding rules . 51. The following practical methods of effecting such a com- bination in the simple case of the movements of two points are useful in scientific illustrations and in certain mechanical arrange- ments . Let two moving ...
Page 42
... preceding section ex- hibits the resultant of two simple harmonic motions , whether of the same period or not . Only , if they are not of the same period , the diagonal of the parallelogram will not be constant , but will diminish from ...
... preceding section ex- hibits the resultant of two simple harmonic motions , whether of the same period or not . Only , if they are not of the same period , the diagonal of the parallelogram will not be constant , but will diminish from ...
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Common terms and phrases
acceleration action algebraic angular velocity anticlastic application Cambridge centre of inertia circle co-ordinates coefficients component configuration constant corresponding course curvature curve cycloidal cylinder degrees of freedom denote determined differential equation direction cosines displacement distance dt dt dt dy dx dy dy dy dy dz dynamical ellipsoid equal equations of motion equilibrium expression finite fluid force formula function give given gyrostatic Hence impulse infinitely small instant integral kinetic energy length linear mass measured momentum moving negative notation osculating plane 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 motions solution space spherical harmonic spherical surface St John's College strain suppose tangent plane theorem tion values whole zero αξ
Popular passages
Page 241 - Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it may be compelled by impressed forces to change that state.