Can anybody try to derive a lagrangian from a system shown in pic related...

I get the potential, but how do you get the kinetic energy?

Are you sure you've got the y coordinate of hte m mass derived correctly? I'm getting a bit different results. Namely for [math] y_{m} = y - l\cos \varphi [/math]

[math] T = \frac{1}{2}M\bigg(1 + \bigg(\frac{\partial y}{\partial x}\bigg)^{2}\bigg)\dot{x}^{2} + \frac{1}{2}ml^{2}\dot{\varphi}^{2} + \frac{1}{2}m\dot{x}^{2}\bigg(\frac{\partial y}{\partial x}\bigg)^{2} + ml\dot{x}\dot{\varphi}\sin \varphi \frac{\partial y}{\partial x} [/math]

Man, sci latex somehow fucks up the size on the derivatives, one more try

[math] T = \frac{1}{2}M(1 + (\frac{\partial y}{\partial x})^{2})\dot{x}^{2} + \frac{1}{2}ml^{2}\dot{\varphi}^{2} + \frac{1}{2}m\dot{x}^{2}(\frac{\partial y}{\partial x})^{2} + ml\dot{x}\dot{\varphi}\sin \varphi \frac{\partial y}{\partial x} [/math]

Okay, I stand corrected. I didn't account for [math] x [/math] in [math] x_{m} [/math]

Excuse for a question, but you couldn't help me to find the program for Windows for input of such symbols?

For anyone still interested, the result giving user was correct, the kinetic energy of the system is given as

[math] T = \frac{1}{2}(M + m)\dot{x}^{2}(1 + (\frac{\partial y}{\partial x})^{2}) + \frac{1}{2}ml^{2}\dot{\varphi}^{2} + ml\dot{x}\dot{\varphi}(\frac{\partial y}{\partial x}\sin \varphi + \cos \varphi ) [/math]

for the coordinates of the object with mass [math] m [/math]

[math]
y_{m} = y - l\cos \varphi
x_{m} = x + l\sin \varphi
[/math]

It's called LaTeX, look up the Veeky Forums latex guide for example.

not op but interested user, can someone run me through the third term?

i know the first term is the kinetic energy of the both masses, multiplied by the change in speed of the trajectory (if s is length, then ds^2=dy^2+dx^2, then ds/dx=sqrt(1+y'^2) ), then kinetic energy term from moment of intertia, then what?, then potential.

It's called LaTeX. I suggest going here: tug.org/texlive/acquire-netinstall.html to download what's called Texlive, which is basically a collection of packages for Latex. It will also install texstudio, which is a text editor geared towards LaTeX editing.

Here's a tutorial series on LaTeX:
youtube.com/watch?v=7HC9xEZsqdM

[math]\displaystyle L=\frac{1}{2}(M+m)\dot{x}^2(1+y'(x)^2)+\frac{1}{2}ml^2\dot{\phi}^2+ml(\dot{x}\dot{\phi})^2(y'(x)\sin{\phi}+\cos{\phi})-(M+m)gy+mgl\cos{\phi}[/math]

ftfy

OR
Open a reply to someone(on Veeky Forums), use the "TEX" button in the left corner and practice, FOR LESS BUTTFUCKING STRESS

Sorry, wrong pic

Let him have the full package, user, the more people who use LaTeX in general, the less shitty papers made in Word we see.

why is the install so fucking massive

Packages. The language packages amount to a few gigs so only get the english (or your language) and that should cut down on space.

anyone got some example latex articles/reports for inspiration?

Since this had some response, I'm giving up another example. I've got the correct solution, so give your shot at it ,if you want, physfellows.

Additionally, derive two integrals of motion from the lagrangian and using the initial conditions, find where are the turning points. The point particle is moving in a cone whose vertex angle is [math]2 \alpha [/math]

Hint: Use the cylindrical coordinates [math] \rho, \varphi, z [/math]