INADEQUACIES

In some cases, our "foundation stones" have been overly idealized.  

Example 1--Chaos

The idea of chaos resulting from simple (though nonlinear) deterministic equations of motion was resisted for years. Gradually, the simple rigid planar pendulum has become the archetype of chaos; and studies of mesodynamic mechanical systems suggest that the "low and slow" (small amplitude, long period) physical pendulum should become an important example of complexity.  Because the internal friction for this case typically involves irreversible mesoscopic structure changes, the complexity is referred to as mesoanelasticity.  A paper describing some experimentally observed examples of these complexities is:  "Experimental evidence for a new frontier--mesoanelastic complexity", Advances in Synergetics, 2, 42-62, IOP Minsk, Belarus (1995).  

Example 2--Damping of Mechanical Systems

The damping term used to describe the dissipated free decay of a simple harmonic oscillator has conventionally been a viscous term; i.e., the friction force of damping is assumed proportional to the first power of the velocity.  Recent experiments with long period pendula show this assumption to be a poor approximation if one wants to consider more than a single frequency of oscillation (one mass configuration of the pendulum).  Whereas viscous damping predicts a first power proportionality in the period of the logarithmic decrement of the motion, actual systems are much closer to quadratic in the period.  A new "flip-flop" model of the pendulum is much more consistent with the observed behavior of the log decrement.  Details may be found in "The Not-So-Simple Harmonic Oscillator", Amer. J. Phys. Vol. 65, No. 11, 1067, (1997) .  

A bigger problem than its failure to agree with experimental data is the fact that the viscous damping assumption is misleading with regard to the physical processes responsible for dissipation of the mechanical energy of oscillation.  For example, a widespread erroneous notion is that air viscosity must be the primary cause of the damping.  Actually, the dominant process is anelastic flexure of the support structure of the pendulum.  

Potential Energy Function:

It is popularly assumed that nonlinear behavior of a pendulum is important only as the amplitude of the motion gets large--a case in which assumed equality of the sine of the angle with the angle is no longer valid.  Studies of pendula in the mesodynamic realm demonstrate that some of the most interesting nonlinear behavior is to be found at very small displacements.  Their observation requires operation of the instrument at long periods of the motion, since the effects of mesoanelastic complexity are small, and the sensitivity of the instrument to forcing is proportional to the square of the period.  When these prerequisites are met (by monitoring the motion, for example, with an SDC sensor), it is possible to discover new properties of the potential energy function.  Instead of being a parabola, as popularly assumed, one finds that the energy function may be "modulated" with metastabilities.  This idea is not so strange when one considers that creep of a long period instrument is hard to avoid.  Creep, in turn, involves atomic rearrangement, a type of "atomic musical chairs".

Negative Damping:

One of the more fascinating observations of a mesodynamics type is that of negative damping.  A long period pendulum can be forced by external means into a  "far-from-equilibrium" condition.  One way this has been done is by exposing load bearing samples (lithium fluoride single crystals) in the structure of the instrument (optically driven pendulum) to a high power argon ion laser. In the flip-flop damping process, normally the circulation of the stress-strain hysteresis loop is clockwise (positive damping). When negative damping occurs, the direction of traversal of the hysteresis will have changed to counterclockwise, and the amplitude of oscillation increases.  This is not so strange in light of the manner in which a mechanical watch continues to tick as long as the mainspring supplies energy through the escapement.  In the case of the pendulum, the energy for oscillation in this negative damping case must come from defect states of the support structures.  Involving dislocations in the grain structures, the process has been labeled "mechanical oscillation by stimulation of excited states" (MOSES).  Currently, the atomic processes (many-body) appear hopelessly complicated to some--a "wilderness" out of which it is hoped that physics may be led by some modern day "champion".

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