Relative Equilibria of Pinwheel Point Mass Systems in a Planar Gravitational Field

Authors

Ritwik Gaur, Wayzata High School, MinnesotaFollow

Abstract

In this paper, we consider a planar case of the full two-body problem (F2BP) where one body is a pinwheel (four point masses connected via two perpendicular massless rods) and the other is a point mass. Relative equilibria (RE) are defined to be ordered pairs (r, θ) such that there exists a rotating reference frame under which the two bodies are in equilibrium when the distance between the point mass and the center of the pinwheel is r and the angle of the pinwheel within its orbit is θ. We prove that relative equilibria exist for all ordered pairs (r, 0) and (r, π/4) where r ∈ ℝ⁺. Additionally, we find conditions under which both of these families of relative equilibria are linearly stable and conditions under which relative equilibria of the form (r, 0) are energetically stable.

Author Bio

Ritwik Gaur is a student at Wayzata High School in Minnesota. His research work studies Pinwheel Point Mass Arrangements and their Relative Equilibria.

Faculty Sponsor

Jodin Morey

Recommended Citation

Gaur, Ritwik (2024) "Relative Equilibria of Pinwheel Point Mass Systems in a Planar Gravitational Field," Rose-Hulman Undergraduate Mathematics Journal: Vol. 25: Iss. 2, Article 2.
Available at: https://scholar.rose-hulman.edu/rhumj/vol25/iss2/2