Energy Stability of Gravitationally Interacting Rods and Dumbbells

We extend classic dynamical results for two or three gravitationally interacting point masses to ideal rods and dumbbells. We derive equilibrium configurations by demanding that the vector of first derivatives of energy at constant angular momentum vanish. We investigate their stability by checking if the spectrum of the Hessian matrix of second derivatives is positive. The additional degrees of freedom allow the objects to store and exchange angular momentum and enable us to elucidate the behavior of non-spherical celestial bodies like asteroids and comet nuclei.