I have the force $F$ shown above. How could I specify the initial values of position ($x$) and speed ($v$) in Mathematica using the
Manipulate command to try finding the initial values so the particle could move on a parabolic trajectory ($\alpha$) and a eight-shaped trajectory ($\beta$) ?
The initial values are not exact, just one solution each is enough.
Unfortunately I have no idea how to realize this problem, would be thankful for help!