Treatise on Natural Philosophy, Part 1University Press, 1886 - Calculators |
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Page xi
... Co - ordinates of a Point - of any system- Generalized Components of Velocity - Examples 183-185 186-190 · 191-194 195-201 202-204 APPENDIX A. - Expression in Generalized Co - ordinates for Poisson's Extension of Laplace's Equation ...
... Co - ordinates of a Point - of any system- Generalized Components of Velocity - Examples 183-185 186-190 · 191-194 195-201 202-204 APPENDIX A. - Expression in Generalized Co - ordinates for Poisson's Extension of Laplace's Equation ...
Page xiii
... Co - ordinates - Generalized Expression for Kinetic Energy -Generalized Components of Force - of Impulse - Im- pulsive Generation of Motion referred to Generalized Co - ordinates - Momentums in terms of Velocities - Kinetic Energy in ...
... Co - ordinates - Generalized Expression for Kinetic Energy -Generalized Components of Force - of Impulse - Im- pulsive Generation of Motion referred to Generalized Co - ordinates - Momentums in terms of Velocities - Kinetic Energy in ...
Page xiv
... Co - ordinates and the Energy ; its differential Coefficients equal re- spectively to Initial and Final Momentums , and to the time from beginning to end - Same Propositions for Ge- neralized Co - ordinates - Hamilton's " Characteristic ...
... Co - ordinates and the Energy ; its differential Coefficients equal re- spectively to Initial and Final Momentums , and to the time from beginning to end - Same Propositions for Ge- neralized Co - ordinates - Hamilton's " Characteristic ...
Page 25
... co - ordinates in its own plane , we have only the equations d2x Px d'y Py = whence , as before , dt γ dt2 r de = h . dt If , by the help of this last equation , we eliminate t from d2x Рx dt2 = substituting polar for rectangular co - ...
... co - ordinates in its own plane , we have only the equations d2x Px d'y Py = whence , as before , dt γ dt2 r de = h . dt If , by the help of this last equation , we eliminate t from d2x Рx dt2 = substituting polar for rectangular co - ...
Page 34
... co - ordinates of two points referred to axes regarded as fixed ; and έ , ŋ , their relative co - ordinates -- we have έ = x ' - x , n = y ' −y , ( = 2 - 2 , and , differentiating , de dx dx dt dt dt " etc. , which give the relative ...
... co - ordinates of two points referred to axes regarded as fixed ; and έ , ŋ , their relative co - ordinates -- we have έ = x ' - x , n = y ' −y , ( = 2 - 2 , and , differentiating , de dx dx dt dt dt " etc. , which give the relative ...
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Common terms and phrases
acceleration action altered angular velocity anticlastic application 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 dy dy dy dz 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 Laplace's equation length moving P₁ parallel parallelepiped particle perpendicular polygon position principal axes 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 whole x₁ y₁ αξ λ² аф