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Super complicated figure, how to proceed? (tikz)

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I need to draw one fairly complicated figure, consisting of several accurately placed ellipses and lines. So far I've been using tikz for drawing graphs and other simple objects, but in this case I have no idea where to start from. Since this looks pretty hard and long, I don't expect you to show me the code, but some guidelines would be more than welcomed. Below I post the figure (drawn by hand) and some explanations:

enter image description here

This is supposed to be a split tube with axis in its center. Also, along the tube in its core there are several identical curves.Basically, I need to draw 4 partial ellipses of appropriate sizes and translate them across the figure. Additionally, I need to draw 5-10 lines (which I assume is fairly easy) and close the inner little curves with semi-circles ideally. However, the hardest part seems to be erasing the parts of the ellipses which should not be visible.

If anyone can help with this, would highly appreciate it.

P.S. It is not necessary to use tikz, if there are better options, I would gladly go with them.

P.S.S. After using various sources and blindly tweaking parameters (we are still new with this), I and my co-worker managed to make this bare resemblance of the original picture:

\begin{tikzpicture}[scale=2] \begin{scope}[rotate=15] \node[transform shape,ellipse,minimum height=2cm,minimum width=1cm,draw,outer sep=0]     (a) {}; \clip[scale=0.8,postaction={line width=0.8pt,draw}] (a) circle (0.5 and 1); \draw[scale=0.8] ([shift={($0.75*({cos(15)},{sin(15)})$)}]a) circle (0.5 and 1); \draw(a.west) -- (a.east); \end{scope} \begin{scope}[rotate=15] \draw (a.north) --  ++(0.75,0) arc (90:-90:0.5cm and 1cm-2\pgflinewidth) -- (a.south); \draw[->] (a.east) ++(0.75,0) -- ++(1cm,0); \draw (a.west) ++(-0.75,0) -- ++(0.9cm,0); \node at (-1,0.2) {$u'_0(t)$}; \end{scope}\end{tikzpicture}

By the way for some reason the "ellipse" module doesn't work on my personal laptop (even though "circle" does), if someone can tell me why would be nice. Have no idea how to proceed further though and what need to learn in order to finish the picture.


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