Jove
Visualize
Contact Us

Related Experiment Videos

Nonautonomous and nonlinear effects in generalized classical oscillators: A boundedness theorem

Ferrari1, Degli Esposti Boschi C

  • 1Dipartimento di Fisica dell'Universita di Bologna and Istituto Nazionale per la Fisica della Materia, Unita di Bologna, viale Berti-Pichat, 6/2, 40127, Bologna, Italy.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
Summary

We proved that certain classical oscillators with symmetric potentials remain bounded, preventing exponential instability. This finding is crucial for understanding the behavior of many physical systems.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Alternating hemiplegia of childhood: no mutations in the familial hemiplegic migraine CACNA1A gene.

Cephalalgia : an international journal of headache·2001
Same author

Cardiac abnormalities in the acquired immunodeficiency syndrome. A prospective study with a clinical-pathological correlation in twenty-one adult patients.

Arquivos brasileiros de cardiologia·2001
Same author

Security concept in 'MyAngelWeb((R))' a website for the individual patient at risk of emergency.

International journal of medical informatics·2001
Same author

Author's Response: In Vivo Measurements of Renal 11ss-Hydroxysteroid Dehydrogenase Type 2 Activity.

The Journal of clinical endocrinology and metabolism·2001
Same author

A new Arabidopsis thaliana root gravitropism and chirality mutant.

Plant science : an international journal of experimental plant biology·2000
Same author

New anilinophthalazines as potent and orally well absorbed inhibitors of the VEGF receptor tyrosine kinases useful as antagonists of tumor-driven angiogenesis

Journal of medicinal chemistry·2000
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Area of Science:

  • Classical Mechanics
  • Mathematical Physics
  • Nonlinear Dynamics

Background:

  • Nonautonomous linear oscillators can exhibit exponential instability.
  • Understanding amplitude and energy boundedness is vital for modeling physical systems.

Purpose of the Study:

  • To rigorously establish boundedness for a class of generalized classical oscillators.
  • To investigate conditions preventing exponential instability in these systems.

Main Methods:

  • Analysis of generalized classical oscillators with symmetric potentials.
  • Focus on systems with a single equilibrium point.
  • Mathematical derivation of boundedness conditions.

Main Results:

  • A rigorous result ensuring amplitude and energy boundedness is presented.

Related Experiment Videos

  • Key factors identified: oscillating solutions and a non-quadratically diverging autonomous potential part.

    • Conclusions:

    • The study provides a theoretical guarantee for the boundedness of specific generalized classical oscillators.
    • This work contributes to the stability analysis of physical systems described by such oscillators.