Orbital dynamics in superfluidHe3. I. Homogeneous systems

A general theory of orbital dynamics is proposed which makes use of a $k$-space time-dependent rotation to take into account the motion of the order parameter. The kinetic equation for Bogoliubov quasiparticles is written. Together with the angular momentum conservation law, this gives a closed set of equations for orbital dynamics. The collisionless regime and the hydrodynamic regime are studied and the results are compared to those of Leggett and Takagi, and of Cross and Anderson. It is shown how, within this theory, orbital dynamics reduces to spin dynamics in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-$B$ and, in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-$A$, for rotations around $\hat{l}$, reduces to the dynamics of the phase of the order parameter.