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The NASA Double Asteroid Redirection Test (DART) mission is a planetary defense-driven test of a kinetic impactor on Dimorphos, the satellite of the binary asteroid 65803 Didymos. DART will intercept Dimorphos at a relative speed of ${\sim}6.5 \text{ km s}^{-1}$, perturbing Dimorphos's orbital velocity and changing the binary orbital period. We present three independent methods (one analytic and two numerical) to investigate the post-impact attitude stability of Dimorphos as a function of its axial ratios, $a/b$ and $b/c$ ($a \ge b \ge c$), and the momentum transfer efficiency $\beta$. The first method uses a novel analytic approach in which we assume a circular orbit and a point-mass primary that identifies four fundamental frequencies of motion corresponding to the secondary's mean motion, libration, precession, and nutation frequencies. At resonance locations among these four frequencies, we find that attitude instabilities are possible. Using two independent numerical codes, we recover many of the resonances predicted by the analytic model and indeed show attitude instability. With one code, we use fast Lyapunov indicators to show that the secondary's attitude can evolve chaotically near the resonance locations. Then, using a high-fidelity numerical model, we find that Dimorphos enters a chaotic tumbling state near the resonance locations and is especially prone to unstable rotation about its long axis, which can be confirmed by ESA's Hera mission arriving at Didymos in late 2026. We also show that a fully coupled treatment of the spin and orbital evolution of both bodies is crucial to accurately model the long-term evolution of the secondary's spin state and libration amplitude. Finally, we discuss the implications of a post-impact tumbling or rolling state, including the possibility of terminating BYORP evolution if Dimorphos is no longer in synchronous rotation., Comment: 38 pages, 13 figures, Accepted for publication in Icarus

The evolution of binary asteroid dynamics are not fully understood. The method of formation is widely accepted as spin-up and fission due to the YORP effect, but it is unclear why systems exist at a variety of energy levels. Binary asteroids are observed in states ranging from relaxed, synchronous equilibriums to chaotic dynamics. Previous planetary encounters may have an effect on the dynamic configuration of binary asteroids. We develop a model for the spherical restricted full three-body problem to simulate a binary asteroid perturbed by a planetary flyby, as well as a method of obtaining initial conditions for a relaxed, singly synchronous binary asteroid system. These are used in a numeric analysis employing a modified version of the General Use Binary Asteroid Simulator, where Monte Carlo simulations are leveraged to investigate how a range of Earth encounters affect the dynamic evolution of a generic binary asteroid system in a singly synchronous equilibrium. The results show that planetary flybys can disrupt the synchronous equilibrium, with the effects dropping off at far encounter distances and fast flyby speeds. After the impulsive perturbation of a planetary flyby, the binary asteroid spin-orbit coupling can prevent the system from settling into a new equilibrium, forcing the system to go through the energy dissipation process to re-equilibrate. It is therefore possible that planetary encounters may have a part in creating chaotic binary asteroid systems from previously relaxed equilibrated systems.