- #1
Nora Fajes
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Hi! I've been trying to find the equation of motion for the simple pendulum using x as the generalized coordinate (instead of the angle), but I haven't been able to get the right solution...
The data is as usual, mass m, length l and gravity g. The X,Y axes origin can be anywhere I choose.
Equation of motion using Lagrange equiations.
This is the solution I'm supposed to find:
[x''+(x*x'^2)/sqrt(l^2-x^2)+(g*x*sqrt(l^2-x^2))/l^2]=0
(Sorry if it's a bit messy, I don't know how to type equations)
But I get other terms I can't get rid of and I don't know what I'm doing wrong... I'd appreciate any help! Thanks!
Edit: The extra term I get is (x'^2*x'')/sqrt(l^2-x^2) and also (2*g*x')/(sqrt(l^2-x^2)) instead of (g*x*sqrt(l^2-x^2))/l^2.
(Still don't know how to post equations)
Homework Statement
The data is as usual, mass m, length l and gravity g. The X,Y axes origin can be anywhere I choose.
Homework Equations
Equation of motion using Lagrange equiations.
The Attempt at a Solution
This is the solution I'm supposed to find:
[x''+(x*x'^2)/sqrt(l^2-x^2)+(g*x*sqrt(l^2-x^2))/l^2]=0
(Sorry if it's a bit messy, I don't know how to type equations)
But I get other terms I can't get rid of and I don't know what I'm doing wrong... I'd appreciate any help! Thanks!
Edit: The extra term I get is (x'^2*x'')/sqrt(l^2-x^2) and also (2*g*x')/(sqrt(l^2-x^2)) instead of (g*x*sqrt(l^2-x^2))/l^2.
(Still don't know how to post equations)
Last edited: