Treatise on Natural Philosophy, Volume 1, Part 1At the University Press, 1879 - 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 becomes the same as the following . A Relative boat crossing a stream is impelled by the oars with uniform velocity relatively to the water , and always towards a fixed point in the opposite bank ; but it is also carried down ...
... problem becomes the same as the following . A Relative boat crossing a stream is impelled by the oars with uniform velocity relatively to the water , and always towards a fixed point in the opposite bank ; but it is also carried down ...
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 Cambridge centre of inertia circle co-ordinates coefficients component configuration constant corresponding course curvature curve cycloidal cylinder degrees of freedom denote determined differential equation direction cosines displacement distance dt dt dt dy dx dy dy dy dy dz dynamical ellipsoid equal equations of motion equilibrium expression finite fluid force formula function give given gyrostatic Hence impulse infinitely small instant integral kinetic energy length linear mass measured momentum moving negative notation osculating plane 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 motions solution space spherical harmonic spherical surface St John's College strain suppose tangent plane theorem tion values whole zero αξ
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.