Hydrogen is one of the few molecules that has been incarcerated in the molecular cage of C ₆₀ to form the endohedral supramolecular complex H ₂ @C ₆₀ . In this confinement, hydrogen acquires new properties. Its translation motion, within the C ₆₀ cavity, becomes quantized, is correlated with its rotation and breaks inversion symmetry that induces infrared (IR) activity of H ₂ . We apply IR spectroscopy to study the dynamics of hydrogen isotopologues H ₂ , D ₂ and HD incarcerated in C ₆₀ . The translation and rotation modes appear as side bands to the hydrogen vibration mode in the mid-IR part of the absorption spectrum. Because of the large mass difference of hydrogen and C ₆₀ and the high symmetry of C ₆₀ the problem is almost identical to a vibrating rotor moving in a three-dimensional spherical potential. We derive potential, rotation, vibration and dipole moment parameters from the analysis of the IR absorption spectra. Our results were used to derive the parameters of a pairwise additive five-dimensional potential energy surface for H ₂ @C ₆₀ . The same parameters were used to predict H ₂ energies inside C ₇₀ . We compare the predicted energies and the low-temperature IR absorption spectra of H ₂ @C ₇₀ .