3
$\begingroup$

I am studying this article 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). I created the same thread on math.stackexchange.com and there I was recommended to duplicate this question here.

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 does the author mean 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.

Is the author here talking 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?

$\endgroup$

1 Answer 1

1
$\begingroup$

Some of this appears to be more colloquial than strict math. Here are my guesses

'square problem' - just means N inputs and N outputs requires a square matrix for transformation

'operations-level forcemodeling' -- crank up all the computers and software on hand

'third-order equations /theory' - most likely taking the analytic equations and using the first three terms in a Taylor or Fourier series expansion.

'phase with respect to Z-axis' -- since you mention Lissajous figures earlier, this probably means the periodic motion along the z-axis described as $z = sin(\omega t + \psi)$

'three by three' - you are correct- another square matrix of size 3,3 .

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.