  Whereas it is easy to reduce the translational symmetry of a molecular system
by using, e.g., Jacobi coordinates the situation is much more involved for the
rotational symmetry. In this paper we address the latter problem using {\it
holonomy reduction}. We suggest that the configuration space may be considered
as the reduced holonomy bundle with a connection induced by the mechanical
connection. Using the fact that for the special case of the three-body problem,
the holonomy group is SO(2) (as opposed to SO(3) like in systems with more than
three bodies) we obtain a holonomy reduced configuration space of topology $
\mathbf{R}_+^3 \times S^1$. The dynamics then takes place on the cotangent
bundle over the holonomy reduced configuration space. On this phase space there
is an $S^1$ symmetry action coming from the conserved reduced angular momentum
which can be reduced using the standard symplectic reduction method. Using a
theorem by Arnold it follows that the resulting symmetry reduced phase space is
again a natural mechanical phase space, i.e. a cotangent bundle. This is
different from what is obtained from the usual approach where symplectic
reduction is used from the outset. This difference is discussed in some detail,
and a connection between the reduced dynamics of a triatomic molecule and the
motion of a charged particle in a magnetic field is established.
