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 · Momental Ellipsoid - Equilibration of Centrifugal Forces— Definition of Principal Axes of Inertia - Principal Axes— Binet's Theorem - Central Ellipsoid - Kinetic ...
... Radius of Gyration -Fly - wheel - Moment of Inertia about any Axis · Momental Ellipsoid - Equilibration of Centrifugal Forces— Definition of Principal Axes of Inertia - Principal Axes— Binet's Theorem - Central Ellipsoid - Kinetic ...
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 ρ = do ds 1 we conclude P dx d'y - dy d'x ( dx2 + dy ) ( 1 ) , . ( 2 ) . Although it is generally convenient , in kinematical and kinetic formulę , to regard time as the independent variable , and all the ...
... radius of curvature , so that 1 ρ = do ds 1 we conclude P dx d'y - dy d'x ( dx2 + dy ) ( 1 ) , . ( 2 ) . Although it is generally convenient , in kinematical and kinetic formulę , to regard time as the independent variable , and all the ...
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
... curve . These lines will form a conical surface . Suppose this to be cut by a sphere of unit radius having its centre at the fixed point . The length of the Integral curvature of a curve ( compare § 136 ,. 9. ] 7 KINEMATICS .
... curve . These lines will form a conical surface . Suppose this to be cut by a sphere of unit radius having its centre at the fixed point . The length of the Integral curvature of a curve ( compare § 136 ,. 9. ] 7 KINEMATICS .
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Common terms and phrases
acceleration action algebraic altered angular velocity anticlastic application axis Cambridge centre of inertia circle co-ordinates coefficients component condition configuration constant corresponding course curvature curve cycloidal cylinder denote determined differential equation direction cosines displacement distance dt dt dx dy dy dy dy dz ellipsoid elongation equal equations of motion equilibrium expression finite fixed force formula function geometrical given gyrostatic harmonic motions Hence impulse infinitely small instant integral kinetic energy length linear momentum moving negative osculating plane P₁ parallel particle perpendicular polygon position principal axes quadratic quadratic function quantity radius ratio rectangular resultant right angles rigid body rolling roots rotation round shear simple harmonic simple harmonic motions solution spherical harmonic spherical surface St John's College strain suppose tangent plane theorem tion values whole Y₁ λ² аф
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.