Most authoritative PDFs begin by defining coordinate frames. For flexible bodies, we use the Mean Axes condition, which minimizes the kinetic energy due to deformation relative to a moving reference frame. The position of any point on the rocket is defined as:
[ \mathbfr = \mathbfR(t) + \mathbfA(t)(\mathbfu + \mathbfw(\mathbfu, t)) ] dynamics and simulation of flexible rockets pdf
Where:
Flexible rockets exhibit coupled structural and flight-dynamics behavior that can degrade stability and control if not properly modeled. This article reviews modeling approaches for structural flexibility, fluid–structure interaction, actuator/servo dynamics, and sensor placement; derives equations of motion for a flexible multibody launch vehicle; describes linearization and modal reduction techniques; details typical simulation workflows; and presents example results illustrating stability margins, bending modes, and guidance–control interactions. Recommendations for validation and guidance for software implementation are provided. Most authoritative PDFs begin by defining coordinate frames
Run an NASTRAN SOL 103 (normal modes analysis) on your rocket FEM. Export the following for the first 10 modes: Export the following for the first 10 modes:
The GNC system requires notch filters at each modal frequency ( \omega_i ) to prevent CSI. A standard notch filter transfer function is: [ H(s) = \fracs^2 + 2\zeta_z \omega_i s + \omega_i^2s^2 + 2\zeta_p \omega_i s + \omega_i^2, \quad \zeta_z \ll \zeta_p ]