Jove
Visualize
Contact Us
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

Related Experiment Videos

New orbits for the n-body problem.

Robert J Vanderbei1

  • 1Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey, USA. rvdb@princeton.edu

Annals of the New York Academy of Sciences
|June 29, 2004
PubMed
Summary
This summary is machine-generated.

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

Diffraction-based sensitivity analysis for an external occulter laboratory demonstration.

Applied optics·2016
Same author

Monochromatic verification of high-contrast imaging with an occulter.

Optics express·2014
Same author

Response surface modeling of Pb(II) removal from aqueous solution by Pistacia vera L.: Box-Behnken experimental design.

Journal of hazardous materials·2009
Same author

On representing and correcting wavefront errors in high-contrast imaging systems.

Journal of the Optical Society of America. A, Optics, image science, and vision·2006
Same author

Horsing around on Saturn.

Annals of the New York Academy of Sciences·2006
Same author

Optimal one-dimensional apodizations and shaped pupils for planet finding coronagraphy.

Applied optics·2005
Same journal

Multiomics Profiling During Autoimmune Demyelination Highlights a Complex Regulatory Role for Ataxin-1 in B Cells.

Annals of the New York Academy of Sciences·2026
Same journal

Global Trends in Light Pollution and Their Relationship With Socioeconomic Factors.

Annals of the New York Academy of Sciences·2026
Same journal

Wired for Corruption: Inter-Brain Synchrony Encodes Bribery-Related Value Information and Predicts Bribery Agreement.

Annals of the New York Academy of Sciences·2026
Same journal

LM-YOLO: A Lightweight Multi-Scale Enhanced Model for Forest Smoke Detection Using Unmanned Aerial Vehicles.

Annals of the New York Academy of Sciences·2026
Same journal

Polyrhythm Perception and Production: A Scoping Review.

Annals of the New York Academy of Sciences·2026
Same journal

DARTS-CNN-BiLSTM: Intelligent Fault Diagnosis for Computer Numerical Control Machine Tool Feed System.

Annals of the New York Academy of Sciences·2026
See all related articles

Researchers numerically discovered many periodic solutions for the n-body problem, finding most are unstable. Simpler solutions are more likely to be stable than complex, exotic ones.

Area of Science:

  • Celestial mechanics
  • Dynamical systems theory

Background:

  • The n-body problem describes the motion of celestial bodies under mutual gravitational influence.
  • Discovering periodic solutions is crucial for understanding long-term orbital dynamics.

Purpose of the Study:

  • To explore minimizing the action functional as a numerical method for finding periodic solutions to the n-body problem.
  • To characterize the stability of discovered solutions, particularly choreographies.

Main Methods:

  • Numerical minimization of the action functional.
  • Analysis of the stability of obtained periodic orbits.

Main Results:

  • A large number of periodic solutions, including choreographies, were discovered.

Related Experiment Videos

  • Most solutions, including nearly all choreographies, were found to be unstable.
  • Unstable solutions appear easier to find than stable ones.

    • Conclusions:

    • Minimizing the action functional is an effective method for discovering periodic solutions to the n-body problem.
    • The prevalence of unstable solutions suggests a bias in numerical discovery methods.
    • Simpler solutions exhibit higher stability compared to more complex or exotic ones.