The "three-body" problem and Euler's collinear solution

The "three-body" problem and Euler's collinear solution
Notes
[u][b]DISCLAIMER[/b][/u][br]Due to the complexity of the computation it's highly advisable you download the applet on a PC and run it with Geogebra classic 5 for desktop.[br]It may happen that, upon changing some parameters, some element crashes and/or disappears. Use the applet at your own risk and keep a working copy before making modification.[br]The applet has not been cleared up and optimized, so following the code and the relations between the elements contained in it could be not simple.[br][size=100][u][b][br]NOTES[br][/b][/u]From order to chaos.[br]It all starts like a perfect day. Everything's in order, peaceful, regular and predictable. But then, without any warning sign, the disaster creeps in and everything turns awry. Quarrels arise. Havoc reigns! (damn butterfly!).[br][br]In the Euler's solution to the three-body problem the bodies start on a line.[br]They can have different masses and their motion will be driven only by their mutual attractive gravitational forces, all pointing to the CM (Center of Mass) of the system.[br][br]With proper initial conditions Euler (De motu rectilineo trium corporum se mutuo attrahentium - 1767) showed that the three bodies follow three co-focal and co-periodic elliptic orbits in which the common focus is the CM.[br]Here's an english translation of Euler's article: [url=https://www.youtube.com/redirect?event=video_description&redir_token=QUFFLUhqbUg5UTByd3FwSUxnc1NFVWk1V0pYOTVUV19sUXxBQ3Jtc0tuVm9maS1hZDVCRC1sdXFmTGtTS0dMd196ZThXTlV1Z0hMSkg0ZlZ5RDhwSm5RM01zNVA2TEhRQl9GLUl5bHNRa1A3WXc0ODZjdm1DRnF3NnJpeFpMaFNGZ1ZmZWRxZTQwdFdCRks0V2hPTmFMMXJVUQ&q=http%3A%2F%2Feulerarchive.maa.org%2Fdocs%2Ftranslations%2FE327en.pdf&v=VyfamuxWYxM]http://eulerarchive.maa.org/docs/tran...[/url][br][br]Euler solution is beautiful and fascinating but, unfortunately, it's also very unstable and the initially ordered configuration soon turns into chaos.[/size][br]

Information: The "three-body" problem and Euler's collinear solution