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Lagrangian for simple pendulum

by Reshma
Tags: lagrangian, pendulum, simple
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Reshma
#1
Nov2-06, 05:08 AM
P: 777
Find the Lagrangian for a simple pendulum of mass m whose point of support moves uniformly on a vertical circle with constant frequency [itex]\omega[/itex] in a uniform gravitational field.

Let 'l' be the length of the pendulum string. Using plane polar coordinates:
Let T be the KE of the pendulum.
[tex]T = {1\over 2}m \left(\dot {r}^2 + r^2\dot{\theta}^2\right)[/tex]
Let V be the PE.
[tex]V = -mgr\cos \theta[/tex]
r = l = constant
I am wondering how to add the angular velocity [itex]\omega[/itex] to the equation of motion. Need help here.
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JohanL
#2
Nov2-06, 05:16 AM
P: 138
how is omega related to theta?
OlderDan
#3
Nov2-06, 08:53 AM
Sci Advisor
HW Helper
P: 3,031
Quote Quote by Reshma
Find the Lagrangian for a simple pendulum of mass m whose point of support moves uniformly on a vertical circle with constant frequency [itex]\omega[/itex] in a uniform gravitational field.

Let 'l' be the length of the pendulum string. Using plane polar coordinates:
Let T be the KE of the pendulum.
[tex]T = {1\over 2}m \left(\dot {r}^2 + r^2\dot{\theta}^2\right)[/tex]
Let V be the PE.
[tex]V = -mgr\cos \theta[/tex]
r = l = constant
I am wondering how to add the angular velocity [itex]\omega[/itex] to the equation of motion. Need help here.
As with your other problem, You need to pick a pair of coordinates. A pair of angles looks good here also.


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