Treatise on Natural Philosophy, Volume 1, Issue 1University Press, 1879 - Calculators |
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Page 52
... particular cases we may have simple harmonic , or uniform circular , motion . ( Compare § 91. ) If the circular motions are in the same direction , the resultant is evidently circular motion in the same direction . This is the case of ...
... particular cases we may have simple harmonic , or uniform circular , motion . ( Compare § 91. ) If the circular motions are in the same direction , the resultant is evidently circular motion in the same direction . This is the case of ...
Page 53
... particular case above delineated is that of a non - reëntrant curve . ) 73. Let the uniform circular motions be in opposite direc- tions ; then , if the periods are equal , we may easily see , as before , § 66 , that the resultant is in ...
... particular case above delineated is that of a non - reëntrant curve . ) 73. Let the uniform circular motions be in opposite direc- tions ; then , if the periods are equal , we may easily see , as before , § 66 , that the resultant is in ...
Page 58
... particular case had been given previously by Lagranget . we take its value 2in ( ' - § ) If , for cos Ρ 2ίπξ ' COS COS 2in + sin 2ίπξ ' 2inέ sin Ρ Ρ Ρ Ρ and introduce the following notation " p 4. = = [ ' + ( 6 ) αε , A 4 , = B 2 0 ...
... particular case had been given previously by Lagranget . we take its value 2in ( ' - § ) If , for cos Ρ 2ίπξ ' COS COS 2in + sin 2ίπξ ' 2inέ sin Ρ Ρ Ρ Ρ and introduce the following notation " p 4. = = [ ' + ( 6 ) αε , A 4 , = B 2 0 ...
Page 59
... particular case ; provided only that F ( x ) has no infinite value in its period . Hence , with this exception , ( 12 ) or either of its equivalents , ( 14 ) , ( 16 ) , is a true arithmetical expression ; and the series which it ...
... particular case ; provided only that F ( x ) has no infinite value in its period . Hence , with this exception , ( 12 ) or either of its equivalents , ( 14 ) , ( 16 ) , is a true arithmetical expression ; and the series which it ...
Page 66
... particular case of the Hypocycloid , it warns us to return to the consideration of these and kindred Trochoids . curves , which give good instances of kinematical theorems , but which besides are of great use in physics generally ...
... particular case of the Hypocycloid , it warns us to return to the consideration of these and kindred Trochoids . curves , which give good instances of kinematical theorems , but which besides are of great use in physics generally ...
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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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