Treatise on Natural Philosophy, Volume 1, Part 1At the University Press, 1879 - Mechanics, Analytic |
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Page 6
... аф " ds equation above , with λ , μ , v substituted for l , m , n , and 1 du 1 dv 7 ds ' 7 ds T for a , , B , Y. we have only to apply the general 1 αλ Tds dv ds 2 Thus we have 7 ' = ( da ) * + ( du ) + ( dr ) 2 , ds dv or T = ds - 2 αλ ...
... аф " ds equation above , with λ , μ , v substituted for l , m , n , and 1 du 1 dv 7 ds ' 7 ds T for a , , B , Y. we have only to apply the general 1 αλ Tds dv ds 2 Thus we have 7 ' = ( da ) * + ( du ) + ( dr ) 2 , ds dv or T = ds - 2 αλ ...
Page 287
... velocities , we have = = dx + dy dy , dy etc. + dx & + etc. αφ dy + etc. аф etc. . ( 1 ) . components or mo- Generalized expression for kinetic energy . Generalized compo- nents of 313. ] 287 DYNAMICAL LAWS AND PRINCIPLES .
... velocities , we have = = dx + dy dy , dy etc. + dx & + etc. αφ dy + etc. аф etc. . ( 1 ) . components or mo- Generalized expression for kinetic energy . Generalized compo- nents of 313. ] 287 DYNAMICAL LAWS AND PRINCIPLES .
Page 288
... аф dy бу = dy184 84 + etc. dy , 84 + do δφ аф dy etc. etc. δψ + Φδφ + etc. v = x ( xda + Y + etc. ..... ( 4 ) , .. ( 5 ) , dy dz Ψ = ΣΧ +2 dy dy dy dx dy Φ = ΣΧ + Y + zda . ( 6 ) . аф аф do etc. etc. of impulse . These quantities , V ...
... аф dy бу = dy184 84 + etc. dy , 84 + do δφ аф dy etc. etc. δψ + Φδφ + etc. v = x ( xda + Y + etc. ..... ( 4 ) , .. ( 5 ) , dy dz Ψ = ΣΧ +2 dy dy dy dx dy Φ = ΣΧ + Y + zda . ( 6 ) . аф аф do etc. etc. of impulse . These quantities , V ...
Page 303
... аф .. ( 26 ) , dy + dh i dy & $ + etc . = dt dv аф do etc. co - ordi- nates . dx where dt denotes what the velocity - component , would be if y , ø , etc. were constant ; being analytically the partial differ- ential coefficient with ...
... аф .. ( 26 ) , dy + dh i dy & $ + etc . = dt dv аф do etc. co - ordi- nates . dx where dt denotes what the velocity - component , would be if y , ø , etc. were constant ; being analytically the partial differ- ential coefficient with ...
Page 306
... аф dT dt = = - Ψψ + Φ ¢ + · ( 2911 ) , Ψψ + Φ ¢ + ( 29 ) . When the kinematical relations are invariable , that is to say , when t does not appear in the equations of condition ( 25 ) , the equations of motion may be put under a ...
... аф dT dt = = - Ψψ + Φ ¢ + · ( 2911 ) , Ψψ + Φ ¢ + ( 29 ) . When the kinematical relations are invariable , that is to say , when t does not appear in the equations of condition ( 25 ) , the equations of motion may be put under a ...
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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.