Transversality Conditions for Boundary Constraints Defined by Differential Equations
Finding the right conditions to optimize journeys through multi-body systems
This paper solves a long-standing puzzle in trajectory optimization: how to find the mathematically optimal path when a spacecraft must satisfy conditions defined by equations rather than fixed points. The solution introduces new rules for when a trajectory satisfies these equation-based constraints, revealing that optimal paths sometimes behave in counterintuitive ways that don't match classical optimization theory.
Space missions to distant planets and asteroids often require trajectories that satisfy complex dynamic constraints—like staying in a certain orbital relationship to multiple bodies. Without these new transversality conditions, engineers can't reliably verify whether a proposed path is truly optimal or just locally good. This work gives mission planners the mathematical foundation to confidently design fuel-efficient routes through the solar system.