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explorer.nb
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(* Content-type: application/vnd.wolfram.mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
(* CreatedBy='Mathematica 10.4' *)
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(* Beginning of Notebook Content *)
Notebook[{
Cell[CellGroupData[{
Cell["CR3BP Explorer", "Title",
CellChangeTimes->{{3.898318951600625*^9, 3.898318966586989*^9},
3.898319021116881*^9},
TextAlignment->Center,
CellLabel->"",ExpressionUUID->"08dce177-24f9-4151-a365-f39e85df6dfc"],
Cell[TextData[StyleBox["Version 0.2\n(c) 2018 Pavel Hajek",
FontSize->14]], "Subtitle",
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Cell[TextData[{
"\t",
StyleBox["Circular Restricted Three Body Problem (CR3BP)",
FontSlant->"Italic"],
" describes the trajectory of a (small) satellite in the gravitation field \
of two (big) celestial bodies that move on circular orbits about their common \
center in a common plane not influenced by the satellite. This problem is \
naturally formulated in rotating coordinates, where the two celestial objects \
are stationary and in a fixed distance. For some energies, one can show the \
existence of a unique periodic orbit (Lyapunov orbit) about a given Lagrange \
point (a critical point of the potential), and one can use the chaotic \
dynamics in the neighborhood of this orbit to systematically search for \
trajectories with prescribed itineraries (by studying iterated Poincare \
sections of stable and unstable manifolds in the adjacent regions). For \
instance, one can look for a trajectory that goes 2 times around the Earth, 5 \
times around the Moon, 3 times around the Earth, 5 times around both the \
Earth and the Moon, and so on. CR3BP Explorer allows you to plot all this in \
real proportions and with given accuracy. See \
https://github.com/p135246/cr3bp-explorer for more details, references, and \
notation (/Documents/CR3BP.pdf)."
}], "Text",
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Cell["\<\
This program was created in a short time for educational purposes and is far \
from being foolproof or elegant (especially computations of Poincare sections \
and the GUI have to be improved)\
\>", "Item",
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Cell["\<\
In a future release the following will be implemented: automated computations \
of intersections, the method of weak stability boundary, more good presets, \
better controls for organizing and patching trajectories together, interval \
arithmetic.\
\>", "Item",
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StyleBox["1.",
FontWeight->"Bold"],
" Evaluate the initialization cell and scroll down to see the GUI.\n",
StyleBox["2.",
FontWeight->"Bold"],
" ",
StyleBox["Zoom-in:",
FontSlant->"Italic"],
" click and hold the left mouse button while drawing a rectangle around the \
chosen area. ",
StyleBox["Zoom out:",
FontSlant->"Italic"],
" click the right mouse button.\n",
StyleBox["3.",
FontWeight->"Bold"],
" Click \[OpenCurlyDoubleQuote]Add Lyapunov orbit\[CloseCurlyDoubleQuote] to \
plot a Lyapunov orbit \n",
StyleBox["4.",
FontWeight->"Bold"],
" Select a Lyapunov orbit in the popup menu and click \
\[OpenCurlyDoubleQuote]Compute Poincare section\[CloseCurlyDoubleQuote] to \
plot the (un)stable manifold and the corresponding Poincare section.\n",
StyleBox["5.",
FontWeight->"Bold"],
" Repeat the process with different parameters and choose what objects to \
display using the check-boxes. If there are too many object, uncheck them and \
click \[OpenCurlyDoubleQuote]Drop hidden\[CloseCurlyDoubleQuote]"
}], "Text",
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Cell[TextData[{
"The default setting is that of ",
StyleBox["Sun-Jupiter",
FontWeight->"Bold"],
". You can try to check \[OpenCurlyDoubleQuote]Real proportions\
\[CloseCurlyDoubleQuote] to see how small these celestial objects are \
compared to their distance (you will have to zoom in to see them).\n\tThe \
default Lagrange point is ",
StyleBox["L2",
FontWeight->"Bold"],
", and you can click \[OpenCurlyDoubleQuote]Add Lyapunov orbit\
\[CloseCurlyDoubleQuote] to plot the corresponding Lyapunov orbit ",
StyleBox["O1",
FontWeight->"Bold"],
" (you may again have to zoom in to see it). \n\tClick \
\[OpenCurlyDoubleQuote]Compute Poincare section\[CloseCurlyDoubleQuote] to \
plot the projection of the part of the stable manifold ",
StyleBox["M1",
FontWeight->"Bold"],
" of ",
StyleBox["O1",
FontWeight->"Bold"],
" (which is a cylinder in the 4D phase space) that starts at ",
StyleBox["O1",
FontWeight->"Bold"],
" and continues around the Sun-Jupiter system until it intersects the left \
horizontal half-plane (which is the projection of the Poincare section ",
StyleBox["U4",
FontWeight->"Bold"],
" in the phase space). Trajectories inside of this cylinder transverse from \
the Outer region through ",
StyleBox["O1",
FontWeight->"Bold"],
" to the Jupiter region in forward time.\n\tSwitch manifold type to \
\[OpenCurlyDoubleQuote]u\[CloseCurlyDoubleQuote] and click \
\[OpenCurlyDoubleQuote]Compute Poincare section\[CloseCurlyDoubleQuote] again \
to plot a similar projection of the unstable manifold ",
StyleBox["M2",
FontWeight->"Bold"],
". Trajectories inside of this cylinder transverse from the Jupiter region \
through ",
StyleBox["O1",
FontWeight->"Bold"],
" to the Outer region in forward time.\n\tThe \
\[OpenCurlyDoubleQuote]Intersection plot\[CloseCurlyDoubleQuote] below the \
spatial plot now shows the first intersections of ",
StyleBox["M1",
FontWeight->"Bold"],
" and ",
StyleBox["M2",
FontWeight->"Bold"],
" with ",
StyleBox["U4",
FontWeight->"Bold"],
", denoted by ",
StyleBox["M1N1",
FontWeight->"Bold"],
" and ",
StyleBox["M2N1",
FontWeight->"Bold"],
", respectively, as they wind up around the whole Sun-Jupiter system \
(generic behaviour). Because we intersect cylinders with a plane (in 4D), we \
see two deformed ellipses (they might be very prolongated and appear as \
bended lines, so another zooming and plotting more points may be needed). \
These ellipses may or may not intersect, which depends on the value of the \
energy. If there is a point in the interior of the intersection of ",
StyleBox["M1N1",
FontWeight->"Bold"],
" and ",
StyleBox["M2N1",
FontWeight->"Bold"],
", then the corresponding trajectory will contain a trip that starts at \
Jupiter, goes once around the whole Sun-Jupiter system, and comes back to \
Jupiter!\n\tTo study more complicated trips, delete the unstable manifold ",
StyleBox["M2",
FontWeight->"Bold"],
" (uncheck ",
StyleBox["M2",
FontWeight->"Bold"],
" in both check-boxes on the left and click \[OpenCurlyDoubleQuote]Drop \
hidden\[CloseCurlyDoubleQuote]), set the field \[OpenCurlyDoubleQuote]n-th \
intersection\[CloseCurlyDoubleQuote] to 2, and click \
\[OpenCurlyDoubleQuote]Compute Poincare section\[CloseCurlyDoubleQuote] \
again. This will plot the unstable manifold (now probably denoted by ",
StyleBox["M3",
FontWeight->"Bold"],
") on its way around the Sun-Jupiter system until it intersects ",
StyleBox["U4",
FontWeight->"Bold"],
" two times. This will produce two ellipses ",
StyleBox["M3N1",
FontWeight->"Bold"],
" and ",
StyleBox["M3N2",
FontWeight->"Bold"],
" in the \[OpenCurlyDoubleQuote]Intersection plot\[CloseCurlyDoubleQuote]. \
Trajectories that lie in the interior of the intersection of ",
StyleBox["M1N1",
FontWeight->"Bold"],
" and ",
StyleBox["M3N2",
FontWeight->"Bold"],
" then contain a trip that starts from Jupiter, goes 2 times around the \
whole Sun-Jupiter system, and then goes back to Jupiter.\n\n",
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