# Homework Help: Holonomic constraints integrating factor question

1. Sep 23, 2009

### eyenkay

Ok, heres the question, have patience with my terrible latex skills...

1. The problem statement, all variables and given/known data
The equations of constraint of the rolling disk:
dx - asin(theta)d(phi) = 0 -> 1.
dy + acos(theta)d(phi) = 0 -> 2.
are special cases of general linear diff-eqs of constraint of the form:
$$\sum$$g_i(x1,...,xn)dxi = 0 -> 3.

A constraint condition of this tupe is holonomic only if an integrating function f(x1,...,xn) can be found that turns it into an exact differential. Clearly the fn. must be such that
$$\delta$$(fg_i)/$$\delta$$x_j = $$\delta$$(fg_j)/$$\delta$$x_i -> 4.

for all i$$\neq$$j. Show that no such integrating factor can be found for either of equations 1 or 2.

2. Relevant equations
above

3. The attempt at a solution
I have found that when I put either equation 1 or 2 into 3, i can cancel the df, and im left with the original equation, but with the sign backwards (ie 1 becomes dx + ..., and 2 becomes dy - ...). I dont know if this actually means anything...

I am wondering if I can possibly arrange eq 4. so that i have something to integrate, and show that f diverges...? I dont know how to show that there is no such f......

Anybody have any tips or ideas?