Elements of Natural Philosophy |
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Page 83
... potential energy is gained , in every possible motion through that configuration . This is the celebrated principle of virtual velocities which Lagrange made the basis of his Mécanique Analytique . 255. To prove it , we have first to ...
... potential energy is gained , in every possible motion through that configuration . This is the celebrated principle of virtual velocities which Lagrange made the basis of his Mécanique Analytique . 255. To prove it , we have first to ...
Page 84
... potential energy is stored up in any pos- sible motion through that configuration . 256. If a material system , under the influence of internal and applied forces , varying according to some definite law , is balanced by them in any ...
... potential energy is stored up in any pos- sible motion through that configuration . 256. If a material system , under the influence of internal and applied forces , varying according to some definite law , is balanced by them in any ...
Page 85
... potential energy stored up as there is work performed by the applied and internal forces in any possible displacement , the equilibrium is neutral , but not unless . If in every possible infinitely small displacement from a position of ...
... potential energy stored up as there is work performed by the applied and internal forces in any possible displacement , the equilibrium is neutral , but not unless . If in every possible infinitely small displacement from a position of ...
Page 90
... potential energy will make up the deficiency of energy which we shall presently calculate in the motions of the centres of inertia . For simplicity , let the longer body be supposed to be at rest before the collision . Then the shorter ...
... potential energy will make up the deficiency of energy which we shall presently calculate in the motions of the centres of inertia . For simplicity , let the longer body be supposed to be at rest before the collision . Then the shorter ...
Page 91
... potential energy when the pendulum reaches its position of greatest deflection . Let this be given by the angle : then the height to which the centre of inertia is raised is ʼn ( 1 - cos 0 ) if h be its distance from the axis . Thus ...
... potential energy when the pendulum reaches its position of greatest deflection . Let this be given by the angle : then the height to which the centre of inertia is raised is ʼn ( 1 - cos 0 ) if h be its distance from the axis . Thus ...
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Common terms and phrases
acceleration action amount angular velocity anticlastic attraction axis called centimetre centre of gravity centre of inertia circle circular co-ordinates component configuration consider constant cord corresponding cosine couple curvature curve cylinder denote density described diagram displacement distance ellipse ellipsoid elongation equal equations equilibrium external point finite fixed point flexure fluid forces acting formulae friction geometrical given force Hence hodograph horizontal inclined infinitely small instant inversely kinetic energy length magnitude mass matter measured moment of inertia momentum moving normal section P₁ parallel parallelogram particle path pendulum perpendicular plane perpendicular portion position pressure principal axes principle produce projection proportional quantity radius radius of gyration reckoned rectangular relative right angles rigid body rotation round shear shell sides simple harmonic motion solid angle space spherical surface spiral square straight line strain stress suppose tangent theorem tion torsion uniform unit vertical weight whole wire