Consider a empty soda can. It can support significant axial compression. Apply a slight lateral force, however, and it buckles. A flexible rocket behaves similarly. During max-q (maximum dynamic pressure), the vehicle bends like a fishing rod. Sensors located in the payload fairing and the engine section will measure different attitudes simultaneously.
To run a flexible simulation on flight hardware, use:
The most dangerous consequence of flexibility is CSI. The flight control system (FCS) uses gyroscopes and accelerometers to measure body rates. If a structural bending mode has a frequency close to the rigid-body control bandwidth, the FCS may interpret the bending as an attitude error and command the engines to correct it. This creates a positive feedback loop, leading to rapid structural divergence and vehicle breakup. Classic examples include early Titan II and Atlas-Centaur flights, which suffered from severe bending mode coupling. dynamics and simulation of flexible rockets pdf
Engineers discretize the rocket into thousands of small elements. This allows them to calculate the mode shapes and natural frequencies of the structure. They turn the physical structure into a mathematical model of mass, stiffness, and damping matrices.
The equations of motion for a flexible rocket are typically derived using Lagrangian mechanics with discretized elastic modes: Consider a empty soda can
[ \mathbfM \ddot\mathbfq + \mathbfC \dot\mathbfq + \mathbfK \mathbfq = \mathbfF\textaero + \mathbfF\textthrust + \mathbfF\textslosh + \mathbfF\textcontrol ]
Where:
Key challenge: Time-varying mass, inertia, and stiffness (as propellant burns), plus changing aerodynamic environment during ascent.
When you watch a massive rocket like the SLS or Starship lift off, it’s easy to view them as rigid, towering monuments of steel and alloy. But to an aerospace engineer, a rocket is anything but rigid. It is a giant, vibrating tuning fork, bending and flexing as it fights against gravity and atmosphere. The most dangerous consequence of flexibility is CSI
If you’ve ever searched for "dynamics and simulation of flexible rockets PDF" to understand this phenomenon, you know the literature is dense with partial differential equations and control theory.
In this post, we are going to strip away the dense math and look at the core concepts: Why rockets bend, why that is dangerous, and how simulation saves the day.