Recent content by RileyF1

I had a go but when solving for dL/dtheta I ended up with some ridiculously long equation, not sure if I did something wrong though. My professor says that the easiest method is to split the cycloid into small straight line segments then calculate what I want for those, not completely sure what...

At the moment I've gotten Vx, Vy and y in terms of θ and subbed them into L = K-U and so I've got L is equal to some θ's and dθ/dt's This may be a stupid question but how do I find dL/dθ and dL/dθ' individually? Like how do I find dL/dθ'? Do I just treat θ as a constant and only take the...

Homework Statement I want to find the equations of motion for a ball traveling down a cycloid under gravity so I can model the brachistochrone problem on matlab. I've looked online everywhere and can only find the equations for x and y with respect to theta (of the cycloid). I'm guessing then...

So I've discovered that it's pretty impossible to solve for the integral of that function when f(x) = x^2. Wolfram alpha seems to think so at least but it works fine for a simpler function like y = x. I want to sub in the equation of a cycloid but I actually have no idea how to get the equation...

Cool, thanks! Exactly what I was after. Was just a dull moment not separating the velocity into x and y components. I'm guessing the next step would be to use separation of variables so it would be dt = ~~~~~~dx and then integrate? That could get messy.

Homework Statement [/B] I'm trying to write a program in MATLAB which demonstrates a tautochrone curve and how the starting point of a ball is irrelevant as to the time it takes to get to the lowest point in the curve (without friction). At the moment I'm just trying to model it using a simple...