Lesson 13
Lagrange's Equations of Motion, Generalized Coordinates, and Review

Name:etp Section:M2 Start Time:12:5:6 Instructor:pate Course:355

1) In order to develop expertise in using Lagrangians we need lots of practice figuring out how to choose 'good' (convenient, easy to work with, etc.) generalized coordinates. Here's another example to consider.

Suppose a particle of mass m can move in a plane and is subject to an attractive central force that can be represented by f = -k/r2. The force always points toward the origin, as shown in the figure to the right.

(i) What would be good generalized coordinate(s) to use if you want to write a Lagrangian and then find the equation(s) of motion for this particle? Please state your choice(s) and briefly explain.

(ii) Given this/these generalized coordinate(s), what would be the expression for the particle's kinetic energy?

(iii) How would you find an expression for the particle's potential energy?



2) Here's another chance to practice choosing 'good' generalized coordinates to construct useful Lagrangians. A disk of mass m and radius R rolls without slipping down the inclined face of a wedge of mass M. The inclined plane makes an angle a with the horizontal. The wedge can slide without friction along the horizontal surface, as shown in the figure.

What would be 'good' generalized coordinates to choose to construct the Lagrangian of this system? Please state and explain your choices. Please also at least mention other choices you considered (and why you ended up not choosing them).



3) What question(s)/topic(s) would you most like to have addressed if we take part of our class time to review/answer questions before the GR?




Below is a space for your thoughts, including general comments about today's assignment (what seemed impossible, what reading didn't make sense, what we should spend class time on, what was "cool", etc.):

You may change your mind as often as you wish. When you are satisfied with your responses click the SUBMIT button.

I received no help from anyone on this assignment.
I received help from someone on this assignment (document in comments section).