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July 11, 2026Communications on Applied Mathematics and ComputationOpen Access

Trifolium Rose as an Analytic Four-Body Choreography

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Authors

MFM. Fernández‐Guasti

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Overview

Analytic four-body choreography describes fixed mass trajectories, highlighting force interactions.

Key Points

  • The aim is to analytically describe the choreographic motion of four equal-mass bodies under specific force conditions.
  • Described the trajectories and interaction forces of four bodies with equal masses in a choreographic motion setup.
  • Analyzed the motion within a trifolium rose periodic orbit, fixing the center of mass at the origin.
  • Established that non-Newtonian forces are linear combinations of attractive and repulsive components.
  • Bodies follow a trifolium rose periodic orbit without collisions, maintaining constant energy and angular momentum.
  • Maintained quantities such as moment of inertia, kinetic energy, and potential energy under equal scaling conditions.
  • Choreography is linked to Pascal’s limaçon four-body choreography, indicating similarity in motion patterns.

Cite This Study

M. Fernández‐Guasti (2026) studied this question.

synapsesocial.com/papers/6a51e329c18d7f28ca5016b9https://doi.org/10.1007/s42967-026-00602-w
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