## 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.

## 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