Treatise on Natural Philosophy, Volume 1, Issue 1University Press, 1879 - Calculators |
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Page 267
... Stable a particular position of equilibrium , and left to itself , it com- brium . mences and continues vibrating , without ever experiencing more than infinitely small deviation in any of its parts , from the position of equilibrium ...
... Stable a particular position of equilibrium , and left to itself , it com- brium . mences and continues vibrating , without ever experiencing more than infinitely small deviation in any of its parts , from the position of equilibrium ...
Page 310
... stable equi- librium due to motion . Examples continued ; C ( a ) , fold- ing door . Hence the equations of motion ... stable , and therefore m ' is in stable equi- librium . Example ( C ) .- A rigid body m is supported on a fixed axis ...
... stable equi- librium due to motion . Examples continued ; C ( a ) , fold- ing door . Hence the equations of motion ... stable , and therefore m ' is in stable equi- librium . Example ( C ) .- A rigid body m is supported on a fixed axis ...
Page 365
... stable equilibrium , it will ever after fundamen vibrate about this configuration , remaining infinitely near it ; infinitely each particle of the system performing a motion which is com- motion posed of simple harmonic vibrations . If ...
... stable equilibrium , it will ever after fundamen vibrate about this configuration , remaining infinitely near it ; infinitely each particle of the system performing a motion which is com- motion posed of simple harmonic vibrations . If ...
Page 366
... stable equi- hold for motion in the neighbourhood of a configuration of un- tion of un- librium . Case of equality among periods . Graphic representa- tion . stable equilibrium . In this case , some or all of the constituent motions are ...
... stable equi- hold for motion in the neighbourhood of a configuration of un- tion of un- librium . Case of equality among periods . Graphic representa- tion . stable equilibrium . In this case , some or all of the constituent motions are ...
Page 369
... stable equilibrium , and left to move subject to resistances proportional to velocities , shows that the whole motion may be resolved , in general determinately , into 2i different motions each 24 VOL . I. small Infinitely either simple ...
... stable equilibrium , and left to move subject to resistances proportional to velocities , shows that the whole motion may be resolved , in general determinately , into 2i different motions each 24 VOL . I. small Infinitely either simple ...
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Common terms and phrases
acceleration action algebraic angular velocity anticlastic application arbitrary axis Cambridge centre of inertia circle co-ordinates coefficients component configuration constant corresponding course curvature curve cycloidal cylinder denote determined differential equation direction cosines displacement distance dt dt dt dy dx dy dy dy dy dz ellipsoid equal equations of motion equilibrium expression finite fixed force formula function give given gyrostatic harmonic motions Hence impulse infinitely small instant integral kinetic energy Lagrange's linear mass measured momentum moving negative P₁ parallel particle path perpendicular polygon position principal axes principle quadratic quadratic function quantity radius rectangular resultant rigid body rolling roots rotation round simple harmonic simple harmonic motions solution spherical harmonic spherical surface St John's College strain suppose tangent plane theorem tion values variable whole Y₁ αξ λ² аф
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