Treatise on Natural Philosophy, Volume 1, Part 1At the University Press, 1879 - Mechanics, Analytic |
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Page xiii
... Radius of Gyration -Fly - wheel - Moment of Inertia about any Axis · · 280 , 281 282-285 286-288 · Momental Ellipsoid - Equilibration of Centrifugal Forces- Definition of Principal Axes of Inertia - Principal Axes- Binet's Theorem ...
... Radius of Gyration -Fly - wheel - Moment of Inertia about any Axis · · 280 , 281 282-285 286-288 · Momental Ellipsoid - Equilibration of Centrifugal Forces- Definition of Principal Axes of Inertia - Principal Axes- Binet's Theorem ...
Page 2
... radius . 6. Any small portion of a curve may be approximately taken as a circular arc , the approximation being closer and closer to the truth , as the assumed arc is smaller . The curva- ture is then the reciprocal of the radius of ...
... radius . 6. Any small portion of a curve may be approximately taken as a circular arc , the approximation being closer and closer to the truth , as the assumed arc is smaller . The curva- ture is then the reciprocal of the radius of ...
Page 3
... radius of curvature , so that 1 do Ρ ds 1 we conclude Ρ dx d'y - dy d2x ( dx2 + dy " ) } ( 1 ) , . ( 2 ) . Although it is generally convenient , in kinematical and kinetic formulas , to regard time as the independent variable , and all ...
... radius of curvature , so that 1 do Ρ ds 1 we conclude Ρ dx d'y - dy d2x ( dx2 + dy " ) } ( 1 ) , . ( 2 ) . Although it is generally convenient , in kinematical and kinetic formulas , to regard time as the independent variable , and all ...
Page 4
... radius of curvature , the direction cosines of the osculating plane , and the tortuosity , of a curve not in one plane , in terms of Cartesian triple co - ordinates , let , as before , So be the angle between the tangents at two points ...
... radius of curvature , the direction cosines of the osculating plane , and the tortuosity , of a curve not in one plane , in terms of Cartesian triple co - ordinates , let , as before , So be the angle between the tangents at two points ...
Page 7
... Suppose this to be cut by a sphere of unit radius having its centre at the fixed point . The length of the curve of intersection measures the integral curvature of the of 9. ] 7 KINEMATICS . Curvature and Tortuosity of a Tortuous Curve.
... Suppose this to be cut by a sphere of unit radius having its centre at the fixed point . The length of the curve of intersection measures the integral curvature of the of 9. ] 7 KINEMATICS . Curvature and Tortuosity of a Tortuous Curve.
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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.