Timeline for Two different Hill equations for space rendezvous
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 20, 2022 at 13:35 | comment | added | Paulo Gil | @DavidHammen That's what I said | |
| Nov 20, 2022 at 1:00 | vote | accept | Sato Yusei | ||
| Nov 19, 2022 at 20:32 | comment | added | Digger | See here for some nice depictions of a commonly used coordinate system. | |
| Nov 19, 2022 at 15:25 | comment | added | David Hammen | @PauloGil The determinant of a transformation matrix from one left-handed coordinate system to another left-handed coordinate system that only involves a rotation is still one. The determinant of a transformation matrix from a left-handed coordinate system to its reflection is still minus one. Using only left-handed coordinate systems is self-consistent, just as is using only right-handed coordinate systems. Problems arise only with mixing and matching. | |
| Nov 19, 2022 at 15:08 | comment | added | Paulo Gil | I only talk about reference frame, not "real life". Yes, the choice of using right-handed reference frames is arbitrary, we could have selected left-handed ones. Yes, we would have to use the left hand, meaning that for the usual determinant rules a minus sign must be added. We could even not forbid left r right-handed reference frames and deal with the sign at vector level: for each axial (aka pseudovector) we include $(-1)^\alpha$ where $\alpha$ is the sign of the determinant of the transformation matrix. But that is really annoying so people prefer to abolish one "hand" | |
| Nov 18, 2022 at 15:44 | comment | added | David Hammen | @PauloGil That move to exclusively using right-handed coordinate systems is surprisingly recent. For example, airports until recently used north-east-up, which is left-handed. The cross product can be consistently defined in terms of left-handed coordinate systems such that $\hat x \times \hat y$ is still equal to $\hat z$ (but you need to use your left hand so that your thumb points along $\hat x$, your index finger along $\hat y$, and your middle finger along $\hat z$). That said, I do agree: Do not use left-handed coordinate systems. | |
| Nov 18, 2022 at 15:26 | comment | added | Paulo Gil | Regarding item (3), never, never use a left-handed coordinate system (tl;dr). The change from or to left-handed coordinate system affects the sign of all vectors defined by cross products, as they are not normal vectors but the result of antisymmetric operators. It is in theory possible to use left-handed reference frames, but the extra work is so large that people decided to use once and for all, only right-handed reference frames and avoid the problem completely. | |
| Nov 18, 2022 at 13:05 | history | edited | David Hammen | CC BY-SA 4.0 |
added 350 characters in body
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| Nov 18, 2022 at 12:54 | comment | added | David Hammen | Do not use the wikipedia page on the CW equations. It does not specify what $x$, $y$, and $z$ mean. | |
| Nov 18, 2022 at 12:53 | history | edited | David Hammen | CC BY-SA 4.0 |
added 374 characters in body
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| Nov 18, 2022 at 12:39 | history | answered | David Hammen | CC BY-SA 4.0 |