The goal of this project is to expand the orbit state representations supported by GMAT. Orbit state representations are used to define orbital initial conditions and GMAT currently supports the following at the time of this writing: Cartesian, Keplerian, Modified Keplerian, Spherical (RA/DEC), Spherical (AZ/EL), and Equinoctial. The table below shows additional proposed state representations.

Proposed New State Representations

This is a list of proposed new state representations, in order of priority. Each is rated high (H), medium (M), or low (L) by "Value" and "Complexity".

Priority | State Type | Description | Value | Complexity | Reference |

1 | Modified Equinoctial | Non-singular element state representation | L | L | |

1 | Incoming Asympote | Hyperbolic state representation for escape trajectories (RA, DEC, C3, …) | H | L | Orbital Mechanics with MATLAB (`rv2hyper.m` ), |

1 | Outgoing Asymptote | (same as Incoming Asymptote) | H | L | (same as Incoming Asymptote) |

2 | Planetographic | Body-fixed spherical latitude and longitude | M | M | |

2 | Planetodetic | Body-fixed latitude/longitude including flattening | M | M | |

2 | Brouwer-Lyddane | Mean Keplerian elements (short, long, J2) | H | H | |

2 | Launch model | Model launch vehicle path from pad to orbit using cubic or quartic motion | H | H | |

2 | TLE | NORAD two line element set | H | H | |

2 | Herrick | (ecc vector, angular momentum vector, n, long.) | L | M | |

2 | Non-singular Keplerian | Non-singular Keplerian-based elements (SMA, E1–E5) | L | L | |

2 | Delaunay | Canonical Keplerian elements (l, g, h, L, G, H) | L | L | |

3 | Kozai | Mean Keplerian elements | M | H | |

3 | Poincare | Canonical Equinoctial elements | L | M | |

3 | Mean equinoctial | Mean Equinoctial elements | L | H |

Resources

- Spec. for existing state representations
- GMAT Math Spec (see sec. 3.1 for existing state representation conversions)
- Geographic elements: GeographicElements.pdf (attached below)
- Modified equinoctial elements: http://www.cdeagle.com/ommatlab/coordinates.pdf
- Asymptote coordinates: http://www.cdeagle.com/ommatlab/coordinates.pdf
- Brouwer-Lyddane mean elements: BrouwerDelaunay.pdf (attached below)
- Delaunay elements: BrouwerDelaunay.pdf (attached below)

Existing Matlab prototype and GMAT code

- GMAT's
`StateConverter`

code is here: http://gmat.svn.sourceforge.net/viewvc/gmat/trunk/src/base/util/StateConversionUtil.cpp - The matlab prototype for state converters in GMAT is contained in the zip file below (
`stateconv.zip`

). The main function is called`stateconv.m`

. I started on the new outgoing asymptote conversion by implementing a preliminary routine that converts from Cartesian to outgoing asymptote. Obviously, we need to write the inverse routine.