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

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**given**as the foundation of a system in any of the sciences . The dynamical use of the Generalized Coordinates of LAGRANGE , and the Vary- ing Action of HAMILTON , with kindred matter , complete the chapter . The third chapter ... Page x

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**given**Rotations • Most general Motion of a Rigid Body Precessional Rotation - Model illustrating Precession of Equi- noxes Free rotation of a Body kinetically symmetrical about an axis Communication of Angular Velocity equally between ... Page xvii

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**given**Functions . V. Mechanical Integration of Linear Differential Equations of the Second Order with Variable Coefficients . VI . Mechanical Integration of the general Linear Differential Equation of any Order with Variable ... Page 8

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**given**curve . Let ! P be the curvature and the tortuosity of the**given**curve , and do an element of its length . Then Jds and frds , each integral extended over any stated length , 7 , of the curve , are respectively the integral ... Page 11

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**given**time is greater or less : and it may be uniform , i.e. , the same at every instant ; or it may be variable . Uniform velocity is measured by the space passed over in unit of time , and is , in general , expressed in feet per ...### 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.