# Lagrange Function for a certain problem

1. Dec 16, 2011

1. The problem statement, all variables and given/known data

A particle of mass m is connected by a massless spring of force constant k and unstressed
length r0 to a point P that is moving along a horizontal circular path of radius a at a
uniform angular velocity ω. Verify the Lagrange-Function!

2. Relevant equations

Could there be a typing error in the book (the book provided the solution which can be seen in the file "function.png". My own solution just differs in the term with r and has 1/2*m*r^2*theta' instead of 1/2*m*r*theta' like shown in the book. However i think my solution is right or can anybody find a mistake?

3. The attempt at a solution

x[1](t):=a*cos(omega*t)#this is the x-coordinate of P
y[1](t):=a*sin(omega*t)#this is the y-coordinate of P
x[2](t):=x[1](t)+r(t)*cos(theta(t))#this is the x-coordinate of m
y[2](t):=y[1](t)+r(t)*sin(theta(t))#this is the y-coordinate of m
T := (1/2)*m*((diff(x[2](t), t))^2+(diff(y[2](t), t))^2)
V :=(1/2)*k*(r-r[0])^2
L=T-V

I attached a drawing of the exercise and two lagrange functions (from the book and my solution) and a Maple file for convenience.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

#### Attached Files:

• ###### Pictures and maple file.zip
File size:
28.9 KB
Views:
36
2. Dec 17, 2011

### Dick

Your answer is almost certainly correct. That term in the books answer doesn't have consistent dimensions with the terms around it.

3. Dec 17, 2011