Treatise on Natural Philosophy, Volume 1At the University Press, 1888 - Mechanics, Analytic |
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Page xiii
... Problems whose data involve Impulses and Velo- cities - General Problem ( compare § 312 ) -Kinetic Energy a minimum in this case - Examples Lagrange's Equations of Motion in terms of Generalized Co- ordinates deduced direct by ...
... Problems whose data involve Impulses and Velo- cities - General Problem ( compare § 312 ) -Kinetic Energy a minimum in this case - Examples Lagrange's Equations of Motion in terms of Generalized Co- ordinates deduced direct by ...
Page 9
... although curious , and not always very easy , geometrical problems occur in connexion with it . We shall say nothing here about the theory of knots , knitting , weaving , Flexible line . Evolute . plaiting , etc. , but 13. ] 9 KINEMATICS .
... although curious , and not always very easy , geometrical problems occur in connexion with it . We shall say nothing here about the theory of knots , knitting , weaving , Flexible line . Evolute . plaiting , etc. , but 13. ] 9 KINEMATICS .
Page 34
... position and motion of the pursuer with regard to the pursued , we must impress on both a velocity equal and opposite to that of the latter , we see motion . at once that the problem becomes the same 34 [ 46 . PRELIMINARY .
... position and motion of the pursuer with regard to the pursued , we must impress on both a velocity equal and opposite to that of the latter , we see motion . at once that the problem becomes the same 34 [ 46 . PRELIMINARY .
Page 35
... problem , there are three cases , figured below . In the first , the boat , moving faster than the current , reaches the desired point ; in the second , the velocities of boat and stream being equal , the boat gets across only after an ...
... problem , there are three cases , figured below . In the first , the boat , moving faster than the current , reaches the desired point ; in the second , the velocities of boat and stream being equal , the boat gets across only after an ...
Page 55
... problem , Fourier's -to find a complex harmonic function expressing a given arbi- trary periodic function , -when once we are assured that the problem is possible ; and when we have this assurance , it proves that the resolution is ...
... problem , Fourier's -to find a complex harmonic function expressing a given arbi- trary periodic function , -when once we are assured that the problem is possible ; and when we have this assurance , it proves that the resolution is ...
Contents
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Common terms and phrases
action altered angular velocity anticlastic B₁ Cambridge centre of inertia change of direction circle co-ordinates coefficients component condition configuration constant corresponding curvature curve cycloidal cylinder degrees of freedom Demy 8vo denote diagram differential equation direction cosines distance dt dt dx dy dx² dy dy dy dz edition ellipse ellipsoid elongation equal equations of motion equilibrium expression finite fixed fluid force function geodetic geometrical given gyrostatic Hence infinitely small initial integral kinetic energy length moving P₁ parallel parallelepiped particle perpendicular polygon position principal axes quadratic function quantity radius ratio rectangular right angles rigid body rolling roots rotation round shear simple harmonic simple harmonic motions simple shear solution spherical harmonic spherical surface strain suppose synclastic tangent plane theorem tion twist values Y₁ αξ λ² аф
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