  The non-symmetrized hyperspherical harmonics method for a three-body system,
composed by two particles having equal masses, but different from the mass of
the third particle, is reviewed and applied to the $^3$H, $^3$He nuclei and
$^3_{\Lambda}$H hyper-nucleus, seen respectively as $nnp$, $ppn$ and
$NN\Lambda$ three-body systems. The convergence of the method is first tested
in order to estimate its accuracy. Then, the difference of binding energy
between $^3$H and $^3$He due to the difference of the proton and the neutron
masses is studied using several central spin-independent and spin-dependent
potentials. Finally, the $^3_{\Lambda}$H hypernucleus binding energy is
calculated using different $NN$ and $\Lambda N$ potential models. The results
have been compared with those present in the literature, finding a very nice
agreement.
