How do you perform trajectory optimization for aircraft performance?

Trajectory optimization finds control and state histories minimizing a cost function subject to dynamics and constraints. Methods: Direct methods (discretize trajectory, solve NLP with SNOPT/IPOPT), Indirect methods (apply Pontryagin minimum principle, solve two-point BVP), Direct collocation (Gauss-Lobatto or pseudospectral), and Dynamic programming for discrete decisions. Applications: Minimum fuel climb profiles, Time-optimal intercept trajectories, Noise-optimal departure procedures, Range optimization with wind, and Regenerative energy descent. Constraints include: Path constraints (speed limits, g limits, terrain), Terminal constraints (runway, formation position), and Control limits. Software tools include GPOPS, DIDO, and custom codes. Results inform procedure design and FMS optimization algorithms.