Treatise on Natural Philosophy, Volume 1, Part 1At the University Press, 1879 - Mechanics, Analytic |
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Page xv
... Root of Determinantal Equation proved 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 ...
... Root of Determinantal Equation proved 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 ...
Page xvi
... Roots with stability - Application of Routh's Theorem - Equal Roots with instability in tran- sitional cases between Stability and Instability - Condi tions of gyrostatic domination - Gyrostatic Links ex- plained - Gyrostatically ...
... Roots with stability - Application of Routh's Theorem - Equal Roots with instability in tran- sitional cases between Stability and Instability - Condi tions of gyrostatic domination - Gyrostatic Links ex- plained - Gyrostatically ...
Page 15
... root of the sum of their squares - and the cosines of the inclination of its direction to the given directions are the ratios of the com- ponents to the resultant . It is easy to see that as ds in the limit may be resolved into dr and ...
... root of the sum of their squares - and the cosines of the inclination of its direction to the given directions are the ratios of the com- ponents to the resultant . It is easy to see that as ds in the limit may be resolved into dr and ...
Page 128
... root of a cubic which has two imaginary roots . Again , on the other hand , let the given displacements be made so as to produce a strain of the body with no angular displacement of the principal axes of the strain . Thus three lines of ...
... root of a cubic which has two imaginary roots . Again , on the other hand , let the given displacements be made so as to produce a strain of the body with no angular displacement of the principal axes of the strain . Thus three lines of ...
Page 129
... roots the equation - 1 + ( 1 − [ Xx ] - [ Yy ] − [ Zz ] ) n + 192 = 0 , - --- whose roots are imaginary if the coefficient of ʼn lies between +2 and 2. Now - 2 is evidently its least value , and for that case the roots are real , each ...
... roots the equation - 1 + ( 1 − [ Xx ] - [ Yy ] − [ Zz ] ) n + 192 = 0 , - --- whose roots are imaginary if the coefficient of ʼn lies between +2 and 2. Now - 2 is evidently its least value , and for that case the roots are real , each ...
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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.