Replace
...
\[Theta]=0.182; w=0; \[Rho]i=4.2; xi=0.0; ui=8.71; adot= -6.4; zi=26.57; om=11.72; ti=0.0; ts=10000;
...
g = NDSolve[..., WorkingPrecision -> MachinePrecision]
with
...
\[Theta]=182/1000;w=0; \[Rho]i=42/10;xi=0;ui=871/100;adot= -64/10;zi=2657/100;om=1172/100;ti=0;ts=10000;
...
g = NDSolve[..., WorkingPrecision -> 64]
Plot[{x[t], x'[t], x''[t]} /. g[[1]], {t, 0, 29.16}]
Plot[{u[t], u'[t], y[t]} /. g[[1]], {t, 0, 29.16}]
Plot[{z[t]} /. g[[1]], {t, 0, 29.16}]
and the overflow problems are no longer reported, but
NDSolve::ndsz: At t == 29.1681...8`64., step size is effectively zero; singularity or stiff system suspected. >>
remains.