Treatise on Natural Philosophy, Volume 1, Part 1At the University Press, 1879 - Mechanics, Analytic |
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Page xv
... negative when Potential Energy is positive for all real Co - ordinates ; positive for some Roots when Potential Energy has negative values ; but always negative for some Roots - Non - oscillatory sub- sidence to Stable Equilibrium , or ...
... negative when Potential Energy is positive for all real Co - ordinates ; positive for some Roots when Potential Energy has negative values ; but always negative for some Roots - Non - oscillatory sub- sidence to Stable Equilibrium , or ...
Page 23
... negative , y = P c COS ( + Q ) , the harmonic curve , or curve of sines . 20 28 лв If μ be positive , y = Pe3 + Q € ̃3 ; and by shifting the origin along the axis of x this can be put in the form 20 y = R ( c® + e ̃ ̈3 ) : 2 ° which is ...
... negative , y = P c COS ( + Q ) , the harmonic curve , or curve of sines . 20 28 лв If μ be positive , y = Pe3 + Q € ̃3 ; and by shifting the origin along the axis of x this can be put in the form 20 y = R ( c® + e ̃ ̈3 ) : 2 ° which is ...
Page 35
... , the parabola . The time of crossing is a u ( 1 — e " ) ' which is finite only for e < 1 , because of course a negative value is inadmissible . Relative motion . 49. Another excellent example of the transformation 3-2 48. ] 35 KINEMATICS .
... , the parabola . The time of crossing is a u ( 1 — e " ) ' which is finite only for e < 1 , because of course a negative value is inadmissible . Relative motion . 49. Another excellent example of the transformation 3-2 48. ] 35 KINEMATICS .
Page 55
... negative integer . Consider the integral F ( x ) dx a2 + x2 c where a , c , c ' denote any three given quantities . dx less than F ( 2 ) [ a2 + a2 ro Its value is dx and greater than F ( ) a2 + x2 , if z and denote the values of x ...
... negative integer . Consider the integral F ( x ) dx a2 + x2 c where a , c , c ' denote any three given quantities . dx less than F ( 2 ) [ a2 + a2 ro Its value is dx and greater than F ( ) a2 + x2 , if z and denote the values of x ...
Page 56
... negative values of i together , and the terms for i = 0 sepa- rately , we have 1 ===== ( a ++ ( x2 + ip ) ' ) = 1 ( 1 2av x = П 2apv π cot { co 2apv cos 2 sin που - - - 1 av x + av π ( x − av ) Р Σπου 2 Cos -- x - av - 2Σ¡ - 1 ¿ 3μ3 ...
... negative values of i together , and the terms for i = 0 sepa- rately , we have 1 ===== ( a ++ ( x2 + ip ) ' ) = 1 ( 1 2av x = П 2apv π cot { co 2apv cos 2 sin που - - - 1 av x + av π ( x − av ) Р Σπου 2 Cos -- x - av - 2Σ¡ - 1 ¿ 3μ3 ...
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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.