Elements of Natural Philosophy |
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Page 27
... co - ordinates as ' complex harmonic functions ' of the time . 85. By far the most interesting case , and by far the simplest , is that of two simple harmonic motions of any periods , whose directions must of course be in one plane ...
... co - ordinates as ' complex harmonic functions ' of the time . 85. By far the most interesting case , and by far the simplest , is that of two simple harmonic motions of any periods , whose directions must of course be in one plane ...
Page 64
... co - ordinates of the centre of inertia , of masses w1 , w1 , etc. , at points ( x , yı , 31 ) , ( X2 , Ya , Za ) , etc. , are given by the following formulae : - = W1X1 + Wzx ̧ + etc. Στοιχ W1 + w2 + etc. = Στ y = Σων Στ Στις = ? Στο ...
... co - ordinates of the centre of inertia , of masses w1 , w1 , etc. , at points ( x , yı , 31 ) , ( X2 , Ya , Za ) , etc. , are given by the following formulae : - = W1X1 + Wzx ̧ + etc. Στοιχ W1 + w2 + etc. = Στ y = Σων Στ Στις = ? Στο ...
Page 79
... co - ordinates of one of these points relatively to lines of reference in fixed directions through the other . It will therefore , in general , depend on three independent co - ordi- nates , which we may conveniently take as the ...
... co - ordinates of one of these points relatively to lines of reference in fixed directions through the other . It will therefore , in general , depend on three independent co - ordi- nates , which we may conveniently take as the ...
Page 94
... co - ordinates specifying the initial configuration , is equal to the corresponding ( generalized ) com- ponent momentum of the actual motion from that configuration : the rate of increase of the action per unit increase of any one of ...
... co - ordinates specifying the initial configuration , is equal to the corresponding ( generalized ) com- ponent momentum of the actual motion from that configuration : the rate of increase of the action per unit increase of any one of ...
Page 97
... co - ordinates , per unit of increase of any other co- ordinate , is equal to the rate of increase of the component momentum relative to the latter per unit increase or diminution of the former co - ordinate , according as the two co - ...
... co - ordinates , per unit of increase of any other co- ordinate , is equal to the rate of increase of the component momentum relative to the latter per unit increase or diminution of the former co - ordinate , according as the two co - ...
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Common terms and phrases
acceleration action amount angular velocity anticlastic attraction axis called centre of gravity centre of inertia circle circular co-ordinates component configuration consider constant cord corresponding cosine couple curvature curve cylinder denote density described diagram displacement distance ellipse ellipsoid elongation equal equations equilibrium external point finite fixed point flexure fluid forces acting formulae friction geometrical given force Hence hodograph horizontal inclined infinitely small instant inversely kinetic energy length magnitude mass matter measured moment of inertia momentum moving normal section P₁ parallel particle path pendulum perpendicular plane perpendicular portion position pressure principal axes principle produce projection proportional quantity radius radius of gyration reckoned rectangular right angles rigid body rotation round shear shell sides simple harmonic motion solid angle space spherical surface spiral square straight line strain stress suppose tangent theorem tion torsion uniform unit vertical weight whole wire