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Counterintuitive Effects in Mechanics
Mark Levi
Penn State University
Abstract:
The magical ability of a spinning top to stay upright fascinated people for many thousands of years and in many civilizations. Clay spinning tops dated to about 6,000 years ago were excavated in Iraq. And for all these millenia another similarly counterintuitive phenomenon went undiscovered until 1908, when Stephenson observed that an upside-down pendulum becomes stable if its pivot is subjected to vertical vibrations (there is no feedback involved). Later other counterintuitive effects were discovered – and used in physical experiments. Traditionally, this subject has been treated by formal computations, sometimes quite long. This is an effective practical tool, but it does not explain what is really going on. As an alternative to this approach, I will give a geometrical explanation of the seemingly mysterious effect in which an inverted multiple pendulum stands upright when its pivot undergoes vertical vibrations. I will also describe the recently discovered “ponderomotive Lorentz force”: a point mass in a rapidly oscillating potential force field behaves as if it were electrically charged and in the presence of magnetic field. This is a purely mathematical effect: there is no electricity or magnetism involved; superficially this looks like the Faraday effect in which a changing electric field generates a magnetic field.
Tuesday, April 7, 2026
11:00AM AP&M 2402
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Randolph E. Bank
Philip E. Gill
Michael Holst
Administrative Contact:
[ Click to Send Email ]
Mark Levi
Penn State University
Abstract:
The magical ability of a spinning top to stay upright fascinated people for many thousands of years and in many civilizations. Clay spinning tops dated to about 6,000 years ago were excavated in Iraq. And for all these millenia another similarly counterintuitive phenomenon went undiscovered until 1908, when Stephenson observed that an upside-down pendulum becomes stable if its pivot is subjected to vertical vibrations (there is no feedback involved). Later other counterintuitive effects were discovered – and used in physical experiments. Traditionally, this subject has been treated by formal computations, sometimes quite long. This is an effective practical tool, but it does not explain what is really going on. As an alternative to this approach, I will give a geometrical explanation of the seemingly mysterious effect in which an inverted multiple pendulum stands upright when its pivot undergoes vertical vibrations. I will also describe the recently discovered “ponderomotive Lorentz force”: a point mass in a rapidly oscillating potential force field behaves as if it were electrically charged and in the presence of magnetic field. This is a purely mathematical effect: there is no electricity or magnetism involved; superficially this looks like the Faraday effect in which a changing electric field generates a magnetic field.
Tuesday, April 7, 2026
11:00AM AP&M 2402