Treatise on Natural Philosophy, Volume 1, Part 1At the University Press, 1879 - Mechanics, Analytic |
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Page xi
... Function " Equation of Continuity " -Integral Equation of Continuity- Differential Equation of Continuity- " Steady Motion " defined . Freedom and Constraint - Of a Point - Of a Rigid Body - Geo- metrical Clamp -- Geometrical Slide ...
... Function " Equation of Continuity " -Integral Equation of Continuity- Differential Equation of Continuity- " Steady Motion " defined . Freedom and Constraint - Of a Point - Of a Rigid Body - Geo- metrical Clamp -- Geometrical Slide ...
Page xiv
... Function of Initial and Final Co - ordinates and the Energy ; its differential Coefficients equal re- spectively to Initial and Final Momentums , and to the time from beginning to end - Same Propositions for Ge- neralized Co - ordinates ...
... Function of Initial and Final Co - ordinates and the Energy ; its differential Coefficients equal re- spectively to Initial and Final Momentums , and to the time from beginning to end - Same Propositions for Ge- neralized Co - ordinates ...
Page 24
... function of x , y , z ; in nature a function of r only . Hence d3y d2x OC -Y- dt * dt = = 0 , etc. , dz dy dr Y 2 C 2 dt dt dz X C dt dt dy dx х dt -y at dt which give on integration Hence at once С ̧x + С ̧y + C ̧≈ = 0 , or the motion ...
... function of x , y , z ; in nature a function of r only . Hence d3y d2x OC -Y- dt * dt = = 0 , etc. , dz dy dr Y 2 C 2 dt dt dz X C dt dt dy dx х dt -y at dt which give on integration Hence at once С ̧x + С ̧y + C ̧≈ = 0 , or the motion ...
Page 38
... function is what we have defined as the argument of the motion . The Epoch in a simple harmonic motion is the interval of time which elapses from the era of reckoning till the moving point first comes to its greatest elongation in the ...
... function is what we have defined as the argument of the motion . The Epoch in a simple harmonic motion is the interval of time which elapses from the era of reckoning till the moving point first comes to its greatest elongation in the ...
Page 39
... function of the time , a quarter of motion . a period earlier in phase than the displacement , and having its maximum value equal to the velocity in the circular motion by which the given function is defined . For , in the fig . of § 53 ...
... function of the time , a quarter of motion . a period earlier in phase than the displacement , and having its maximum value equal to the velocity in the circular motion by which the given function is defined . For , in the fig . of § 53 ...
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.