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The dynamical integrity concept for interpreting/predicting experimental behaviour: from macro- to nano-mechanics. (English) Zbl 1392.70035
Summary: The dynamical integrity, a new concept proposed by J. M. T. Thompson, and developed by the authors, is used to interpret experimental results. After reviewing the main issues involved in this analysis, including the proposal of a new integrity measure able to capture in an easy way the safe part of basins, attention is dedicated to two experiments, a rotating pendulum and a micro-electro-mechanical system, where the theoretical predictions are not fulfilled. These mechanical systems, the former at the macro-scale and the latter at the micro-scale, permit a comparative analysis of different mechanical and dynamical behaviour. The fact that in both cases the dynamical integrity permits one to justify the difference between experimental and theoretical results, which is the main achievement of this paper, shows the effectiveness of this new approach and suggests its use in practical situations.
“The men of experiment are like the ant, they only collect and use; the reasoners resemble spiders, who make cobwebs out of their own substance. But the bee takes the middle course: it gathers its material from the flowers of the garden and field, but transforms and digests it by a power of its own. Not unlike this is the true business of philosophy (science); for it neither relies solely or chiefly on the powers of the mind, nor does it take the matter which it gathers from natural history and mechanical experiments and lay up in the memory whole, as it finds it, but lays it up in the understanding altered and digested. Therefore, from a closer and purer league between these two faculties, the experimental and the rational (such as has never been made), much may be hoped.”
(Francis Bacon 1561–1626)
“But are we sure of our observational facts? Scientific men are rather fond of saying pontifically that one ought to be quite sure of one’s observational facts before embarking on theory. Fortunately those who give this advice do not practice what they preach. Observation and theory get on best when they are mixed together, both helping one another in the pursuit of truth. It is a good rule not to put overmuch confidence in a theory until it has been confirmed by observation. I hope I shall not shock the experimental physicists too much if I add that it is also a good rule not to put overmuch confidence in the observational results that are put forward until they have been confirmed by theory.”
(Arthur Stanley Eddington 1882–1944)

MSC:
70K50 Bifurcations and instability for nonlinear problems in mechanics
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
70K20 Stability for nonlinear problems in mechanics
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