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The Quarterly Journal of Mechanics and Applied Mathematics 1950 3(4):452-458; doi:10.1093/qjmam/3.4.452
© 1950 by Oxford University Press
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THE CHARACTERISTICS OF SYSTEMS WHICH ARE NEARLY IN A STATE OF NEUTRAL STATIC STABILITY

W. J. DUNCAN

( College of Aeronautics Cranfield, Beds )

It is shown that the rate of subsidence or divergence {lambda} of a system which is near a state of neutral static stability can easily be calculated from a knowledge of the mode of displacement in the neutral state and this mode is found by solving a set of linear algebraic equations. The first-order correction to the mode can also be found and in important cases this can be made the basis for calculating a second approximation to {lambda}; if necessary a further correction to the mode can now be found and from this a still more accurate root can be calculated. The method can be extended to continuous systems having infinitely many degrees of freedom.


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