Theory

Explanations of the mathematics and modelling choices behind FLAPJAX. Unlike the tutorials and how-tos, these pages are discussion, not action — they exist to build intuition and to make design decisions traceable.

• Nonlinear beam Geometrically-exact Cosserat beam on \(\mathrm{SE} (3)\): strain measure, residual, tangent stiffness, and generalised-\(\alpha\) time integration.

• UVLM Unsteady vortex lattice method: bound and wake circulations, regularised Biot–Savart, non-penetration BC, wake convection, and force projection.

• Coupling Partitioned FSI with Aitken-accelerated Picard iteration; static and dynamic variants; convergence criteria.

• Linear Linearisation about a nonlinear equilibrium: modal analysis, aerodynamic state-space, and the coupled aero-augmented eigenproblem used for flutter.

• Adjoint Discrete adjoint for static and dynamic coupled problems; reuse of the primal tangent; checkpointing; design-variable ravel/unravel.