# Homework Help: Solving for Angular momentum without mass

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1. Nov 24, 2014

### thestrangequark

1. The problem statement, all variables and given/known data
The problem is a Lagrangian problem that solves for a differential equation. I need to write a program to solve the Lagrangian numerically. My professor said you do not need mass for the program, but I'm not sure how. The problem is a vertical cone with a bead rolling around the cone. I drew it:
http://puu.sh/d4sN4/37c910ca4f.png [Broken]
In the diagram, θ is the angle displacement of the bead. Here is a vertical view to show θ.
http://puu.sh/d4t13/e7de35cb2e.png [Broken]
the variables are r and θ. x_0, dx/dt, dy/dt are all given. α=45 degrees. Assume θ_0 =0, implying y_0=0

2. Relevant equations
Solving for the Lagrangian gives:
d^2r/dt^2 =(L^2*sin^2α)/(m^2*r^3)-gsinα*cosα
d/dt(mr^2*dθ/dt)=0 showing angular momentum is conserved.

3. The attempt at a solution
Is it as simple as plugging L=mr^2*dθ/dt into the differential equation for r''? This would cancel out the masses in that equation, but I feel like that is too simple and I am missing something.

Last edited by a moderator: May 7, 2017
2. Nov 24, 2014