Treatise on Natural Philosophy, Volume 1, Part 1At the University Press, 1879 - Mechanics, Analytic |
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Page xiv
... Quadratic Functions to Sums of Squares - Gene- ralized Orthogonal Transformation of Co - ordinates - Sim- plified expressions for the Kinetic and Potential Energies --Integrated Equations of Motion , expressing the fun- damental modes ...
... Quadratic Functions to Sums of Squares - Gene- ralized Orthogonal Transformation of Co - ordinates - Sim- plified expressions for the Kinetic and Potential Energies --Integrated Equations of Motion , expressing the fun- damental modes ...
Page xvi
... Quadratics , provided that gyrostatic in- fluence be fully dominant - Limits of smallest and second smallest of the four periods - Limits of the next greatest and greatest of the four periods Quadruply free Cycloidal System with non ...
... Quadratics , provided that gyrostatic in- fluence be fully dominant - Limits of smallest and second smallest of the four periods - Limits of the next greatest and greatest of the four periods Quadruply free Cycloidal System with non ...
Page 288
... quadratic function of 4 , 4 , etc. , when expressed in terms of generalized co - ordinates , so that if we denote it by T we have i + $$ T = } { ( 4 , v ) * + ( , ) $ * + ... +2 ( , ) + ... } ...... ( 2 ) , where ( 4 , 4 ) , ( 4 , 4 ) ...
... quadratic function of 4 , 4 , etc. , when expressed in terms of generalized co - ordinates , so that if we denote it by T we have i + $$ T = } { ( 4 , v ) * + ( , ) $ * + ... +2 ( , ) + ... } ...... ( 2 ) , where ( 4 , 4 ) , ( 4 , 4 ) ...
Page 290
... quadratic function of 4 , 4 , etc. , we have 2T = S + n + gô + etc. we have by differentiation .. ( 9 ) . From this , on the supposition that T , 4 , 4 , ... are expressed in terms of έ , n , .... dT 2 = + + ξ di do dė + η αξ de de + t ...
... quadratic function of 4 , 4 , etc. , we have 2T = S + n + gô + etc. we have by differentiation .. ( 9 ) . From this , on the supposition that T , 4 , 4 , ... are expressed in terms of έ , n , .... dT 2 = + + ξ di do dė + η αξ de de + t ...
Page 303
... quadratic transforma- function of the generalized velocity - components with functions the equa- of the co - ordinates as coefficients as shown in § 313 ( 2 ) ] that the motion in d d differentiations and in ( 23 ) are performed ...
... quadratic transforma- function of the generalized velocity - components with functions the equa- of the co - ordinates as coefficients as shown in § 313 ( 2 ) ] that the motion in d d differentiations and in ( 23 ) are performed ...
Contents
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acceleration action algebraic altered angular velocity anticlastic application axis Cambridge centre of inertia circle co-ordinates coefficients component condition configuration constant corresponding course curvature curve cycloidal cylinder denote determined differential equation direction cosines displacement distance dt dt dx dy dy dy dy dz ellipsoid elongation equal equations of motion equilibrium expression finite fixed force formula function geometrical given gyrostatic harmonic motions Hence impulse infinitely small instant integral kinetic energy length linear momentum moving negative osculating plane P₁ parallel particle perpendicular polygon position principal axes quadratic quadratic function quantity radius ratio rectangular resultant right angles rigid body rolling roots rotation round shear simple harmonic simple harmonic motions solution spherical harmonic spherical surface St John's College strain suppose tangent plane theorem tion values whole Y₁ λ² аф
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.