Dynamic analysis and optimization design of ignition attitude for an internally carried air-launch rocket

This paper focuses on the dynamic analysis and optimization design of the ignition attitude, which characterizes the motion of an internally carried air-launch (ICAL) rocket from separation to ignition. Mismatches in the ICAL system parameters or initially loose constraints can result in an inappropriate ignition attitude that poses significant risks to both the carrier aircraft and the rocket. A three-body quaternion dynamic model is developed to describe the ignition attitude of the ICAL, with the mechanical properties of the bridle reformulated using a Y-shaped distributed mass–spring-damping model. The Runge–Kutta–Munthe–Kaas (RKMK) quaternion integration method is employed to circumvent explicit algebraic constraints and differential algebraic equations (DAEs) while solving the three-body dynamics. To attain the desired ignition attitude and eliminate failure modes, the ICAL parameter design is formulated as a multi-objective optimization problem. The Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is then used to determine the optimal ignition attitude and design variables under constraints on ignition condition, bridle deformation and tension conditions. Simulation results from the proposed dynamic model exhibit trends consistent with the T/Space second test data, where the nose-up motion peaks and the pitch angle subsequently oscillates around maximum after the parachute release. Among three failure modes examined, insufficient damping and initial slack of the bridle lead to oscillations and recurrent transient losses in tension, while parameters mismatches cause bridle deformations to exceed acceptable limits. By balancing the three objectives, the optimization identifies the optimal design that features an ignition pitch angle closer to 90°, less altitude loss, and more stable oscillations with weak attenuation. As a result, the optimization meets the ignition attitude requirement of the ICAL and effectively avoids the third failure mode.