Lagrangian for simple pendulum


by Reshma
Tags: lagrangian, pendulum, simple
Reshma
Reshma is offline
#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.
Phys.Org News Partner Science news on Phys.org
NASA's space station Robonaut finally getting legs
Free the seed: OSSI nurtures growing plants without patent barriers
Going nuts? Turkey looks to pistachios to heat new eco-city
JohanL
JohanL is offline
#2
Nov2-06, 05:16 AM
P: 141
how is omega related to theta?
OlderDan
OlderDan is offline
#3
Nov2-06, 08:53 AM
Sci Advisor
HW Helper
P: 3,033
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.


Register to reply

Related Discussions
Accelerating Elastic Pendulum (Lagrangian) Advanced Physics Homework 0
Foucault Pendulum - Lagrangian Advanced Physics Homework 0
Simple Pendulum Motion and Physical Pendulum Introductory Physics Homework 6
among Simple harmonic oscillation, simple pendulum and physical pendulum Introductory Physics Homework 10
Pendulum problem using Lagrangian approach Introductory Physics Homework 6