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

### From inside the book

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**Axes**- Composition of Rota- tions and Translations in One Plane - Superposition of Small Motions - Rolling of ...**axis**Communication of Angular Velocity equally between Inclined SECTIONS 78-94 95-101 · 102 , 103 • 104-107 108**Axes**... Page xii

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**Axis**- Moment of a whole Motion round an**Axis**- Re- sultant**Axis**• Virtual Velocity - Virtual Moment Work - Practical Unit - Scientific Unit - Work of a Force- Work of a Couple - Transformation of Work - Potential Energy - • 235 , 236 ... Page xiii

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**Axis**· Momental Ellipsoid - Equilibration of Centrifugal Forces— Definition of Principal**Axes**of Inertia - Principal**Axes**— Binet's Theorem - Central Ellipsoid - Kinetic Symmetry round a Point ; round an**Axis**Energy in Abstract Dynamics ... Page 14

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**axis**of x , and so by v , w , for the other two ; dx dy dz we have u = " dt v = dt ' w = Hence , calling a , ß , y the dt • angles which the direction of motion makes with the**axes**, and ds putting q = we have dt ' dx dx dt и COS α ... Page 20

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**axes**is proportional to its distance from that**axis**, the path is an ellipse or hyperbola whose principal diameters coincide with those**axes**; and the acceleration is directed to or from the origin at every instant . dx dt = 1 , dy dt ...### 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.