Every isochronous potential is shear-equivalent to a harmonic potential

Every isochronous potential is shear-equivalent to a harmonic potential Harmonic oscillations are isochronous, but so are oscillations in any potential that is shear-equivalent to a harmonic potential. We demonstrate the converse: that every possible isochronous potential is shear-equivalent to a harmonic potential. To do this we show that every potential is shear-equivalent to a unique symmetric potential, and that every isochronous symmetric potential is harmonic. Shearing is thus the only possible period-preserving transformation for potentials with fixed energy. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png American Journal of Physics American Association of Physics Teachers

Every isochronous potential is shear-equivalent to a harmonic potential

Loading next page...
 
/lp/aapt/every-isochronous-potential-is-shear-equivalent-to-a-harmonic-5ftGR0Ic6M
Publisher
American Association of Physics Teachers
Copyright
© 2018 American Association of Physics Teachers.
ISSN
0002-9505
D.O.I.
10.1119/1.5019025
Publisher site
See Article on Publisher Site

Abstract

Harmonic oscillations are isochronous, but so are oscillations in any potential that is shear-equivalent to a harmonic potential. We demonstrate the converse: that every possible isochronous potential is shear-equivalent to a harmonic potential. To do this we show that every potential is shear-equivalent to a unique symmetric potential, and that every isochronous symmetric potential is harmonic. Shearing is thus the only possible period-preserving transformation for potentials with fixed energy.

Journal

American Journal of PhysicsAmerican Association of Physics Teachers

Published: Mar 17, 2018

There are no references for this article.

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve Freelancer

DeepDyve Pro

Price
FREE
$49/month

$360/year
Save searches from
Google Scholar,
PubMed
Create lists to
organize your research
Export lists, citations
Read DeepDyve articles
Abstract access only
Unlimited access to over
18 million full-text articles
Print
20 pages/month
PDF Discount
20% off