Treatise on Natural Philosophy, Volume 1, Part 1At the University Press, 1879 - Mechanics, Analytic |
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Page xvi
... Algebraic Theorem SECTIONS 344-345xxvili Kinetic Stability - Conservative disturbance of motion - Ki- netic Stability and Instability discriminated - Examples -Circular Simple Pendulum - Kinetic Stability in Cir- cular Orbit - Kinetic ...
... Algebraic Theorem SECTIONS 344-345xxvili Kinetic Stability - Conservative disturbance of motion - Ki- netic Stability and Instability discriminated - Examples -Circular Simple Pendulum - Kinetic Stability in Cir- cular Orbit - Kinetic ...
Page 30
... algebraic curve . The axis of x is easily seen to be an asymptote if e 1 . х 41. When a point moves in any manner , the line joining it with a fixed point generally changes its direction . If , for simplicity , we consider the motion as ...
... algebraic curve . The axis of x is easily seen to be an asymptote if e 1 . х 41. When a point moves in any manner , the line joining it with a fixed point generally changes its direction . If , for simplicity , we consider the motion as ...
Page 36
... algebraic equation between x and y whenever ∞ and @ 1 are commensurable . - Thus , for w1 = 2w , suppose wt = 0 , and we have x = a cos 0 + b cos 20 , y = a sin 0 + b sin 20 , or , by an easy reduction , ( x2 + y3 − b3 ) 2 = a2 { ( x ...
... algebraic equation between x and y whenever ∞ and @ 1 are commensurable . - Thus , for w1 = 2w , suppose wt = 0 , and we have x = a cos 0 + b cos 20 , y = a sin 0 + b sin 20 , or , by an easy reduction , ( x2 + y3 − b3 ) 2 = a2 { ( x ...
Page 50
... algebraic . If not , they are transcendental . 68. From the above we see generally that the composition of any number of simple harmonic motions in any directions and of any periods , may be effected by compounding , according to ...
... algebraic . If not , they are transcendental . 68. From the above we see generally that the composition of any number of simple harmonic motions in any directions and of any periods , may be effected by compounding , according to ...
Page 128
... algebraic process , we find - - ( [ Xx ] − n ) ( [ Yy ] − n ) ( [ Z≈ ] − n ) - - - − [ Y2 ] [ Zy ] ( [ Xx ] − n ) − [ Zx ] [ X2 ] ( [ Yy ] −n ) − [ Xy ] [ Yx ] ( [ Zz ] − n ) + [ Xz ] [ Yx ] [ Zy ] + [ Xy ] [ Yz ] [ Zx ] = 0 ...
... algebraic process , we find - - ( [ Xx ] − n ) ( [ Yy ] − n ) ( [ Z≈ ] − n ) - - - − [ Y2 ] [ Zy ] ( [ Xx ] − n ) − [ Zx ] [ X2 ] ( [ Yy ] −n ) − [ Xy ] [ Yx ] ( [ Zz ] − n ) + [ Xz ] [ Yx ] [ Zy ] + [ Xy ] [ Yz ] [ Zx ] = 0 ...
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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.