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

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**Rolling**of Curve on Curve - Cycloids and Trochoids - Properties of the Cycloid - Epicycloid , Hy- pocycloids , etc. Motion of a Rigid Body about a Fixed Point - Euler's Theorem -Rodrigues ' Co - ordinates - Composition of Rotations ... Page 8

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**rolling**, which will be treated afterwards ( §§ 110-137 ) . But it is enough at present to remark , that if a plane roll on the sphere , along the spherical curve , turning always round an instantaneous axis tangential to the sphere ... Page 36

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**rolling**of a circle on a fixed straight line or circle . In the mean time , we take a different form of enunciation , which , however , leads to precisely the same result . Find the actual path of a point which revolves uniformly in a ... Page 44

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**rolling**of a turret ship at sea , the marching of troops over a suspension bridge , etc. 62. If any number of pulleys be so placed that a cord pounding passing from a fixed point half round each of them has its free parts all in ... Page 53

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**rolling**of one circle Composi- tion of two uniform circular motions . on another . ( The particular case above delineated is that of a non - reėntrant curve . ) 73. Let the uniform circular motions be in opposite direc- tions ; then ...### 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.