Treatise on Natural Philosophy, Volume 1, Issue 1University Press, 1879 - Calculators |
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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
... 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 . SECTIONS 1,
... 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 . SECTIONS 1,
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 ...
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Common terms and phrases
acceleration action algebraic angular velocity anticlastic application arbitrary axis Cambridge centre of inertia circle co-ordinates coefficients component configuration constant corresponding course curvature curve cycloidal cylinder denote determined differential equation direction cosines displacement distance dt dt dt dy dx dy dy dy dy dz ellipsoid equal equations of motion equilibrium expression finite fixed force formula function give given gyrostatic harmonic motions Hence impulse infinitely small instant integral kinetic energy Lagrange's linear mass measured momentum moving negative P₁ parallel particle path perpendicular polygon position principal axes principle quadratic quadratic function quantity radius rectangular resultant rigid body rolling roots rotation round simple harmonic simple harmonic motions solution spherical harmonic spherical surface St John's College strain suppose tangent plane theorem tion values variable whole Y₁ αξ λ² аф
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