Treatise on Natural Philosophy, Volume 1, Part 1At the University Press, 1879 - Mechanics, Analytic |
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Page xiv
... Function of Initial and Final Co - ordinates and the Energy ; its differential Coefficients equal re- spectively to ... Quadratic Functions to Sums of Squares - Gene- ralized Orthogonal Transformation of Co - ordinates - Sim ...
... Function of Initial and Final Co - ordinates and the Energy ; its differential Coefficients equal re- spectively to ... Quadratic Functions to Sums of Squares - Gene- ralized Orthogonal Transformation of Co - ordinates - Sim ...
Page 288
... quadratic function of 4 , 4 , etc. , when expressed in terms of generalized co - ordinates , so that if we denote it ... functions of the co - ordinates , determinable according to the conditions of the system . The only condition ...
... quadratic function of 4 , 4 , etc. , when expressed in terms of generalized co - ordinates , so that if we denote it ... functions of the co - ordinates , determinable according to the conditions of the system . The only condition ...
Page 290
... functions of the last - named elements . And , since T is a 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 ...
... functions of the last - named elements . And , since T is a 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 ...
Page 303
... quadratic transforma- function of the generalized velocity - components with functions the equa- of the co ... function of t , 4 , 4 , 0 , etc. Using ( 26 ) in ( 22 ) we now find instead of a homogeneous quadratic function of 4 , 4 ...
... quadratic transforma- function of the generalized velocity - components with functions the equa- of the co ... function of t , 4 , 4 , 0 , etc. Using ( 26 ) in ( 22 ) we now find instead of a homogeneous quadratic function of 4 , 4 ...
Page 306
... quadratic function , and ,, ... each a linear function , of these elements , with coeffi- cients - functions of 4 , 4 , etc. , depending on the kinematical conditions of the system , but not on the particular motion . Thus , denoting ...
... quadratic function , and ,, ... each a linear function , of these elements , with coeffi- cients - functions of 4 , 4 , etc. , depending on the kinematical conditions of the system , but not on the particular motion . Thus , denoting ...
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Common terms and phrases
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.