Lagrangian Mechanics: Would a Block Fall Off a Parabolic Path?

[@dogspaghetti7118]

I love this guy lmao. He’s like your eclectic uncle you get to see on the holidays

[@fizixx]

I'm going to have to print the final value of lambda and also do the plot from 0 to 0.1, or 0.01, just to see what's happening, but it's interesting how the shape changes this behavior.

[@frogstud]

For an object in free fall we have y = g/2 * (v_x * t)^2 so a = g * v_x^2 / 2. So a perfectly fitting parabola would depend on both g and initial velocity in the x direction. Interestingly enough parabolas like this only intersect at the origin so if we have a large enough initial x velocity the object leaves the curve never to return.