# More Help With Lagrangian Mechanics

cmmcnamara
So in my internet readings on Lagrangian mechanics I started researching applications with non-potential and/or non-conservative forces and came across this page:

http://farside.ph.utexas.edu/teaching/336k/Newton/node90.html

This page is fascinating but I'm having a bit of difficulty understanding a piece of the first example. Can some one explain to me the constraint function they came up with? Its labeled as equation 727. I feel like I'm missing something obvious but I just can't figure it out. Thank you!

## Answers and Replies

Studiot
Isn't this the no slip condition?

That is in words

The distance (χ) down the plane = the angle turned through by the cylinder times the radius

Precisely: If the cylinder is rolling without slipping the distance, travelled of a fixed point from the initial time, where we set $\phi=0$ is given by the circumference along the cylinder boundary, i.e., it's $a \phi$, where $a$ is the cylinder's radius. The same distance the cylinder's center axis has travelled, i.e., we must have the constraint
$$x=a \phi,$$
where we have chosen $x=0$ as an initial condition. The constraint function is then given (up to a sign and an overall multiplicative constant, which both are irrelevant for the solution of the problem) thus reads in this case as given by Eq. (727).