Treatise on Natural Philosophy, Volume 1, Issue 1At the University Press, 1879 - Mechanics, Analytic |
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Page 4
... turning about the tangent to the curve . The tortuosity is therefore to be measured by the rate at which the osculating plane turns about the tangent , per unit length of the curve . To express the radius of curvature , the direction ...
... turning about the tangent to the curve . The tortuosity is therefore to be measured by the rate at which the osculating plane turns about the tangent , per unit length of the curve . To express the radius of curvature , the direction ...
Page 7
... turns during the motion of the point exhibits what we have thus defined as the integral curvature . In estimating this , we must of course take the enlarged modern meaning of an angle , including angles greater than two right angles ...
... turns during the motion of the point exhibits what we have thus defined as the integral curvature . In estimating this , we must of course take the enlarged modern meaning of an angle , including angles greater than two right angles ...
Page 8
... turning always round an instantaneous axis tangential to the sphere , the integral curvature of the curve of contact or trace of the rolling on the plane , is a proper measure of the whole torsion , or integral of tortuosity . From this ...
... turning always round an instantaneous axis tangential to the sphere , the integral curvature of the curve of contact or trace of the rolling on the plane , is a proper measure of the whole torsion , or integral of tortuosity . From this ...
Page 20
... turns in unit of time ; then , by properly choosing the axes , we have whence dx dt dy == a sin at , = a cos at , dt ( x − A ) 2 + ( y — B ) 2 = a2 - b . If a point moves in a plane , and if its component velo- city parallel to each of ...
... turns in unit of time ; then , by properly choosing the axes , we have whence dx dt dy == a sin at , = a cos at , dt ( x − A ) 2 + ( y — B ) 2 = a2 - b . If a point moves in a plane , and if its component velo- city parallel to each of ...
Page 28
... turns during that interval . There is a corresponding theorem for a planet moving in an ellipse , but somewhat more com- plicated . Curves of pursuit . 40. If two points move , each with a definite uniform velo- city , one in a given ...
... turns during that interval . There is a corresponding theorem for a planet moving in an ellipse , but somewhat more com- plicated . Curves of pursuit . 40. If two points move , each with a definite uniform velo- city , one in a given ...
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Common terms and phrases
acceleration according action actual altered amount angle angular velocity application axes axis becomes body called Cambridge centre circle co-ordinates coefficients complete component condition configuration consider constant corresponding course curvature curve denote described determined differential direction displacement distance edition equal equations equilibrium Example expression finite fixed force function give given harmonic Hence inertia infinitely small instant integral kinetic energy length less mass matter mean measured motion moving natural negative observations parallel particle particular path period perpendicular plane position present principle problem produced proved quantity radius reference relative remain remarkable respectively resultant rigid rolling roots rotation round side simple solution space spherical strain suppose surface tangent theorem tion turn unit University values whole
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.