Path for the 0.1 release

[jorgepiloto]

This issue collects all the objectives to be accomplished in order to achieve the 0.1 release. The project layout is depicted, together with the main chapters to be implemented. This issue is subjected to modifications as time evolves.

Chapters of the document

• 1 Introduction to this work

  • 1.1 Problem description and motivation
    The problem to be solved is introduced together with the main motivation behind it.

  • 1.2 Objectives and goals achieved
    A list of objectives and goals is provided as a brief resume for reader.

  • 1.3 Real-world applications
    Applications in the past, such us the routines employed by the AGC are exposed to reader together with more modern ones. As and example, a porkchop contour map for Earth-Mars in 2020 is included, showing the most optimal point of transfer, which is coincident with the latest missions to the Martian planet.

  • 1.4 Social and economical analysis
    A data set of launches is presented and sorted by the nature of the misison, showing a clear increase in the communications sector. In addition, a timeline for published articles about Lambert's problem is provided.

• 2 Review of Lambert's problem

  • 2.1 The problem to be solved
    The Lambert's problem is introduced again. By justifying the necessity of only 3DoF, the problem is then moved to the fundamental plane of the orbit PQW.

  • 2.2 The orbital plane

    • 2.2.1 Solving the h vector
    • 2.2.2 Solving the orbit's inclination
    • 2.2.3 Solving the RAAN of the orbit

  • 2.3 Lambert's theorem and implicit solution

    • 2.3.1 The differential vis-viva equation form
    • 2.3.2 Series solution to the differential vis-viva equation

  • 2.4 Geometry of the solutions to the problem
    The conics to the solutions are presented: elliptic, parabolic or hyperbolic ones. Justification on when those exist depending on the number of revolutions and the time of flight is provided together with a graphical analysis.

    • 2.4.1 Elliptic solutions
    • 2.4.2 Parabolic solutions
    • 2.4.3 Hyperbolic solutions
    • 2.4.4 Singularities

  • 2.5 Classic analytical solutions

• 3 Modern Lambert's solvers

  • 3.1 Introduction to modern solvers
    The start of modern solvers in the 60s due to computers usage. Lancaster work about Lambert's problem.

  • 3.2 Modern solver's structure

  • 3.3 Classification
    Regarding the free-parameter (iteration variable) a classification can be performed according to it. Some algorithms inherit from others.

  • 3.4 Solvers input and output parameters
    Describe all the required input and output parameters of any Lambert's problem solver implemented in the form of a computer routine.

• 4 A new method based on conic equations

• 5 Performance comparison

• 6 Results and conclusions