  We suggest that random matrix theory applied to a classical action matrix can
be used in classical physics to distinguish chaotic from non-chaotic behavior.
We consider the 2-D stadium billiard system as well as the 2-D anharmonic and
harmonic oscillator. By unfolding of the spectrum of such matrix we compute the
level spacing distribution, the spectral auto-correlation and spectral
rigidity. We observe Poissonian behavior in the integrable case and Wignerian
behavior in the chaotic case. We present numerical evidence that the action
matrix of the stadium billiard displays GOE behavior and give an explanation
for it. The findings present evidence for universality of level fluctuations -
known from quantum chaos - also to hold in classical physics.
