Treatise on Natural Philosophy, Volume 1, Issue 1University Press, 1879 - Calculators |
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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 dx dt == a sin at , dy dt = a cos at , Examples of accelera- tion . whence ( x − A ) ' + ( y − B ) * = a2 . - a b . If a point moves in a plane , and if its ...
... turns in unit of time ; then , by properly choosing the axes , we have dx dt == a sin at , dy dt = a cos at , Examples of accelera- tion . whence ( x − A ) ' + ( y − B ) * = a2 . - a b . If a point moves in a plane , and if its ...
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 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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