## Treatise on Natural Philosophy, Volume 1, Part 1At the University Press, 1879 - Mechanics, Analytic |

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**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 rde , where r and are polar co - ordinates of a plane curve , dr dt do and r dt are the resolved parts of the velocity ... Page 34

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**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**BGA G'A or has a constant value . Then GB G'B G ' A G 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

... 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 Kelvin (1st baron), Peter Guthrie Tait. and the

William Thomson Kelvin (1st baron), 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 ... Page 79

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**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 ...### Contents

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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.