Comparison of minimum-propellant guidance laws for impulsive and bounded-thrust spacecraft

The minimum-propellant deterministic guidance law for a bounded-thrust, constant jet exhaust velocity rocket is compared to the minimum-propellant impulsive-thrust guidance law. It is shown that the impulsive-thrust guidance law represents the limit of the bounded-thrust guidance law as the magnitude of the thrust acceleration becomes unbounded (a → ∞) and the thrust duration goes to zero (τ → 0). This connection is of more than academic value in that it eases the interpretation of the bounded-thrust guidance law in terms of the much more easily understood impulsive-thrust case. Of importance is the insight provided towards the interpretation of the jump conditions and controllability condition in the one-burn case.