TY - JOUR
T1 - Geometrical aspects of rapid vibrations and rotations
AU - Levi, Mark
N1 - Funding Information:
Data accessibility. This article does not contain any additional data. Competing interests. I declare I have no competing interests. Funding. Partially supported by NSF grant no. DMS-9704554. Acknowledgements. The author is grateful to two anonymous referees for some very helpful comments which helped improve the exposition.
Publisher Copyright:
© 2019 The Author(s).
PY - 2019/11/18
Y1 - 2019/11/18
N2 - The counterintuitive phenomenon of stabilization of the inverted pendulum by the vertical vibration of its pivot has been known for over a century. This remarkable effect attracted attention of many mathematicians and physicists, including Kapitsa, Feynman, Arnold, Moser and others. The 1989 Nobel Prize in Physics was awarded to W. Paul for his discovery of the particle trap based on this phenomenon. The inverted pendulum is a tip of an 'iceberg' of related phenomena arising in systems with high-frequency time-dependence. This article surveys some related phenomena discovered more recently, some connections with differential geometry and mechanics, and some new geometrical insights.
AB - The counterintuitive phenomenon of stabilization of the inverted pendulum by the vertical vibration of its pivot has been known for over a century. This remarkable effect attracted attention of many mathematicians and physicists, including Kapitsa, Feynman, Arnold, Moser and others. The 1989 Nobel Prize in Physics was awarded to W. Paul for his discovery of the particle trap based on this phenomenon. The inverted pendulum is a tip of an 'iceberg' of related phenomena arising in systems with high-frequency time-dependence. This article surveys some related phenomena discovered more recently, some connections with differential geometry and mechanics, and some new geometrical insights.
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U2 - 10.1098/rsta.2019.0014
DO - 10.1098/rsta.2019.0014
M3 - Review article
AN - SCOPUS:85073210184
SN - 1364-503X
VL - 377
JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
IS - 2158
M1 - 20190014
ER -