Treatise on Natural Philosophy, Volume 1, Issue 1University Press, 1879 - Calculators |
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Page vii
... given as the foundation of a system in any of the sciences . The dynamical use of the Generalized Cöordinates of LAGRANGE , and the Vary- ing Action of HAMILTON , with kindred matter , complete the chapter . The third chapter ...
... given as the foundation of a system in any of the sciences . The dynamical use of the Generalized Cöordinates of LAGRANGE , and the Vary- ing Action of HAMILTON , with kindred matter , complete the chapter . The third chapter ...
Page x
... given Rotations Most general Motion of a Rigid Body Precessional Rotation - Model illustrating Precession of Equi- noxes . • SECTIONS 78-94 95-101 102 , 103 • 104-107 · Free rotation of a Body kinetically symmetrical about an axis ...
... given Rotations Most general Motion of a Rigid Body Precessional Rotation - Model illustrating Precession of Equi- noxes . • SECTIONS 78-94 95-101 102 , 103 • 104-107 · Free rotation of a Body kinetically symmetrical about an axis ...
Page 7
... given by the preceding formulæ . Curvature and tortu- osity . curvature ( compare 10. The integral curvature , or whole change of direction of Integral an arc of a plane curve , is the angle through which the tangent of a curve has ...
... given by the preceding formulæ . Curvature and tortu- osity . curvature ( compare 10. The integral curvature , or whole change of direction of Integral an arc of a plane curve , is the angle through which the tangent of a curve has ...
Page 8
... given curve . The average curvature is , as in the case of a plane curve , the integral curvature divided by the ... given curve . Let be the curvature and the tortuosity of the given - P curve , and ds an element of its length . Then ...
... given curve . The average curvature is , as in the case of a plane curve , the integral curvature divided by the ... given curve . Let be the curvature and the tortuosity of the given - P curve , and ds an element of its length . Then ...
Page 11
... given time is greater or less : and it may be uniform , i.e. , the same at every instant ; or it may be variable . Uniform velocity is measured by the space passed over in unit of time , and is , in general , expressed in feet per ...
... given time is greater or less : and it may be uniform , i.e. , the same at every instant ; or it may be variable . Uniform velocity is measured by the space passed over in unit of time , and is , in general , expressed in feet per ...
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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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