[ [M] \ddotq + [C] \dotq + [K] q = Q_thrust + Q_aero + Q_control ]
Use Google Scholar with the exact phrase "flexible rocket" dynamics simulation filetype:pdf . Combine with keywords like "modal truncation" or "notch filter stability" .
Where:
No discussion of is complete without addressing CSI. The control system uses gyroscopes and accelerometers to measure attitude. However, these sensors also measure structural vibration.
# Modal dynamics (forced oscillation) modal_ddot = -2*zeta_bend*omega_bend*modal_vel - omega_bend**2*modal_disp + phi_sensor*control_torque dynamics and simulation of flexible rockets pdf
The dynamics and simulation of flexible rockets are challenging problems that require significant advances in multiple disciplines. Some of the current challenges and future research directions include:
To simulate a flexible rocket, engineers must merge rigid-body dynamics with structural dynamics. The total displacement of any point on the rocket is the sum of its rigid-body motion and its elastic deformation. [ [M] \ddotq + [C] \dotq + [K]
If you're looking for the foundational "manual" on this topic, several key texts and papers outline these modern formulations: (Barrows & Orr): The definitive textbook used by NASA and industry engineers to build flight-ready simulations.