Register to reply

When can the Lagrangian be used

by dsdsuster
Tags: lagrangian
Share this thread:
Apr13-12, 11:20 PM
P: 30
Hello. I have a question about when the Lagrangian can be used. In the textbook we are using it is shown that for constraint forces which do no work, the Lagrangian is of the form T-U. In this question though, it seems like rod would provide a normal force that is in the same direction as the bead's instantaneous velocity at all times.

A bead of mass m is threaded on a frictionless, straight rod which lies in a
horizontal (x-y so no change in gravitational potential energy of the bead) plane and is forced to spin with constant angular velocity ω about a vertical axis through the midpoint of the rod.

Writing out the Lagrangian equations of motion, I get the same result as if the bead were always subject to a radial centripetal force mrw^2. I would basically like to know why the Lagrangian can be used in this case, when the constraining force seems to do work.

Thanks for your help!
Phys.Org News Partner Physics news on
Physical constant is constant even in strong gravitational fields
Physicists provide new insights into the world of quantum materials
Nuclear spins control current in plastic LED: Step toward quantum computing, spintronic memory, better displays
Apr14-12, 01:36 AM
P: 452
Centripetal forces do no work.
Apr14-12, 03:21 AM
P: 30
The radius of the circular path the bead is taking is changing though. Doesn't this imply work is being done?

Register to reply

Related Discussions
Derive that the lagrangian in classical phyics is L=T-V Classical Physics 27
Lagrangian math help Introductory Physics Homework 6
Looking for Lagrangian Systems with Higher Order Time Derivatives in the Lagrangian Special & General Relativity 1
Lagrangian... anyone know their Lagrangian mechanics? Advanced Physics Homework 7
Why Lagrangian only contain q and dq/dt? Classical Physics 13