  We present explicitly Poisson structures, for both time-dependent and
time-independent Hamiltonians, of a dynamical system with three degrees of
freedom introduced and studied by Calogero et al [2005]. For the
time-independent case, new constant of motion includes all parameters of the
system. This extends the result of Calogero et al [2009] for semi-symmetrical
motion. We also discuss the case of three bodies two of which are not
interacting with each other but are coupled with the interaction of third one.
