Treatise on Natural Philosophy, Part 1University Press, 1886 - Calculators |
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Page 15
... ratios of the com- ponents to the resultant . It is easy to see that as ds in the limit may be resolved into dr and r88 , where r and are polar co - ordinates of a plane curve , de dt dr and r dt result thus , are the resolved parts of ...
... ratios of the com- ponents to the resultant . It is easy to see that as ds in the limit may be resolved into dr and r88 , where r and are polar co - ordinates of a plane curve , de dt dr and r dt result thus , are the resolved parts of ...
Page 34
... ratio the line joining them . Let A and B be any simultaneous positions of the points . Take G or G ' in AB such that the ratio B GA G'A A G or has a constant value . Then GB G'B as the form of the relative path depends only upon the ...
... ratio the line joining them . Let A and B be any simultaneous positions of the points . Take G or G ' in AB such that the ratio B GA G'A A G or has a constant value . Then GB G'B as the form of the relative path depends only upon the ...
Page 72
... direction of its axis is found ( § 27 ) , as follows : -The square of the resultant angular velocity is the sum of the squares of its components , and the ratios of the three components to the resultant 72 [ 95 . PRELIMINARY .
... direction of its axis is found ( § 27 ) , as follows : -The square of the resultant angular velocity is the sum of the squares of its components , and the ratios of the three components to the resultant 72 [ 95 . PRELIMINARY .
Page 73
William Thomson Baron Kelvin, Peter Guthrie Tait. and the ratios of the three components to the resultant are the Composi- direction cosines of the axis . tion of angu- lar veloci- ties about axes meet- Hence simultaneous rotations about ...
William Thomson Baron Kelvin, Peter Guthrie Tait. and the ratios of the three components to the resultant are the Composi- direction cosines of the axis . tion of angu- lar veloci- ties about axes meet- Hence simultaneous rotations about ...
Page 79
... ratio to the angular velocity w of the rigid body about its instantaneous axis . 105. The motion of the plane containing these axes is called the precession in any such case . What we have denoted by is the angular velocity of the ...
... ratio to the angular velocity w of the rigid body about its instantaneous axis . 105. The motion of the plane containing these axes is called the precession in any such case . What we have denoted by is the angular velocity of the ...
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Common terms and phrases
acceleration action altered angular velocity anticlastic application B₁ Cambridge centre of inertia change of direction circle co-ordinates coefficients component condition configuration constant corresponding curvature curve cycloidal cylinder degrees of freedom Demy 8vo denote diagram differential equation direction cosines distance dt dt dx dy dy dy dy dz ellipse ellipsoid elongation equal equations of motion equilibrium expression finite fixed fluid force function geodetic geometrical given gyrostatic Hence infinitely small initial integral kinetic energy Laplace's equation length moving P₁ parallel parallelepiped particle perpendicular polygon position principal axes quantity radius ratio rectangular right angles rigid body rolling roots rotation round shear simple harmonic simple harmonic motions simple shear solution spherical harmonic spherical surface strain suppose synclastic tangent plane theorem tion twist values whole x₁ y₁ αξ λ² аф