Hi. Given equations of constraint for the motion of a particle in the form:

$\displaystyle \sum_{i=1}^{n} g_{i}(x_{1},...,x_{n} ) dx_{i} = 0$

will be holonomic only if exists a function $\displaystyle f(x_{1},..,x_{n})$ such that:

$\displaystyle \frac{\partial fg_{i}}{\partial x_{j}} = \frac{\partial fg_{j}}{\partial x_{i}}$ for all $\displaystyle i \neq j$.

In the particular case of:

$\displaystyle dx - a sin(\theta) d\phi =0$

$\displaystyle dy + a cos (\theta) d\phi = 0$

I should find an integrating factor of the form $\displaystyle f(x,y,\theta,\phi)$, but I don't know wich are exactly the $\displaystyle g_{i}$ functions. There are four $\displaystyle g_{i}$.

Thanks for your time.