HERDING INSTINCT
Many physicists pride themselves in being independent thinkers. Oftentimes one hears that 'getting them to work together is like trying to herd cats' . A recent EDS television commercial shows that 'pokes' on horseback can get the majority of a 'gaggle' of cats moving, because of terror, in one direction (with a divergence less than 3.1416, it would appear). There are, however, mavericks that refuse to participate in correlated motion, even borne of fear. Had Ed Lorenz been a physicist, he no doubt would have been one of those mavericks, as evidenced by his now famous talk, "Predictability: Does the Flap of a Butterfly's Wings in Brazil Set off a Tornado in Texas? (Dec. 1972 meeting of the Amer. Assoc. for the Advancement of Science, Wash. D.C."
In spite of Lorenz's work providing a strong warning against the limitations of linearity, the author's mesodynamic studies show a strong unwillingness to depart from conventional wisdom in relationship to small motions of macrosopic oscillators. In particular, there is a widespread naive expectation that the potential well of the SHO is parabolic. Because of their determination to design systems that work, engineers long ago uncovered evidence for the fact that the harmonic potential is not really applicable to macro-oscillators. A linear equation of motion is just not capable of fully describing the damping of these systems. Some individuals have tried to make the linear equation work by employing a continuum of relaxation times. Of course, with an infinity of parameters it is possible to fit anything. To those who were educated before the advent of the standard model, this unrealistic application of mathematics is reminiscent of early confusion in the world of nuclear physics.
A recently published model of mechanical oscillator damping finally provides a simple nonlinear equation of motion that appears to work. Thus it has the blessing of Occam's razor. It assumes that secondary creep (not the popularly assumed primary form) is responsible for a modified (amplitude dependent) Coulomb type of internal friction (structural) damping. If the claims of this paper have any bearing on truth, it is amazing that so little progress has been made toward a theoretical understanding of internal friction damping since the time of Charles Coulomb--who is best known not for his seminal contributions to friction but rather for his law of electrostatic forces.