I am studying the arcticle on orbital mechanics and can't understand the meaning of some terms related to mathematics (perhaps because my native language doesn't have such terms).
1.
The user constructs a targeting scheme [in the program] consisting of independent targeting variables (components of the impulses) and dependent variables (targeting goals). Generally a scheme is constructed such that the number of independent variables equals the number of dependent variables to provide the differential corrector [DC] with a 'square' problem to solve.
'square' problem – here the author means a system of equations where the number of unknown variables is equal to the number of equations in the system?
2.
Swingby [the programm] propagates trajectories numerically with full operations-level force modeling invoked.
I don't have any ideas.
3.
In his development of the third-order solution to the equations of motion for LPOs, Richardson shows...
I don't understand the phrase "third-order solution". The author is talking about "solution of a third-order equations"?
4.
In summary, given the four parameters of the desired Lissajous, the third-order theory yields the state coordinates of the desired target insertion point.
Can the author here talk about a theory based on equations (probably differential) of the third order?
5.
The angle phi is measured in the RLP [a reference frame] xy-plane clockwise from the -x-axis, and the angle psi is the phase with respect to the z-axis.
I don't have any ideas.
6.
However the departure burn and the Z-burn are differentially corrected simultaneously, making for a 3-by-3 differential correction problem.
3-by-3 problem – could it be a system of three equations with three unknown variables?
7.
... position calculated by the third order approximation.
This is a phraseology (like the phrase "zeroth-order approximation" for a very inaccurate solution) or reference to third order polynomium approximation?