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Birkhoff Transcription #1000

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Summary

Added the new birkhoff transcription as laid out by Mike Ross in https://arxiv.org/abs/2308.01400v2

Related Issues

  • Resolves #

Backwards incompatibilities

None

New Dependencies

None

kaushikponnapalli and others added 30 commits August 15, 2023 11:58
…he defects. ex_brachistochrone working. birkhoff_iter_group not yet integrated.
… to better match the referenced. Updated partials.
robfalck and others added 27 commits September 20, 2023 15:31
…ment_ends:x (x_ab = [x_a x_b].

The last is always a design variable, but it is now constrained to match x_a at the start and x_b at
the end.  This will facilitate state jumps at the end of phases.

x_ab will also be more easily turned into a segment-by-segment variable, with a size of (num_segs, 2, shape).
…tates:x, instead of the endpoint values from states:x.
…, but currently only works with fd/cs derivs and a modified version of openmdao
…O#3030) is addressed. Sparse partials are still problematic but it works with cs/fd
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