Among the roughly one in six near-Earth asteroids that travel in pairs, predicting long-term motion has long been a problem that quietly defeats conventional mathematics — shapes and spins entangle in ways that cause simulations to drift and ultimately lie. A team at Liaoning University has answered this with a Hamel variational integrator, a framework that refuses to separate rotation from position, treating the two as a single geometric truth. Published in Space: Science & Technology, the method preserves energy and structural integrity across long orbital timescales while demanding less com