Seeding From a File
Let (n + 1) distinct samples be provided in a *.nod Initial Guess File, in the tabular form 
. Here, fi could be either a dynamical state, mass, or a thrust attitude representation at Ti. You can estimate these quantities at the collocation nodes using one of the following two procedures:
Global Lagrange Interpolation
- Construct an nth: degree interpolating polynomial
based on Lagrange polynomials from the data 
: - Transform the (N + 1) collocation nodes from the standard quadrature interval to the physical interval
, following the transformation: - Test
using Eq. (1). This re-sampled data is passed on to the direct-transcription-collocation system as an initial guess.
where the Lagrange polynomial 
is associated with the data 
in the sense:
(2)
and can be expressed as the node polynomial:
(3)
For more details, see Maneuver Optimization Using Direct Transcription Methods.
Piecewise linear Interpolation
In this case, straight line segments are passed between consecutive pairs of initial guess data points 
and . For 
, test
from:
Seeding from a Finite Maneuver
Seeding from a finite maneuver involves resampling a propagated finite-maneuver ephemeris at the collocation nodes. A propagated ephemeris typically contains many more samples compared to data from an Initial Guess File, and as such, we prefer interpolation using piecewise polynomials, rather than a single, high-order one. Astrogator uses a 7th-order, sliding-window, local Lagrange interpolator for this purpose.