  The equivalence class of absolute configurations of a system under the group
of similarity transformations $Sim(3)$ is called the shape of the system. The
$Sim(3)$ invariant Lagrangian of the modified Newtonian theory ensures the
existence of the its law of motion on shape space. To deduce the equations of
motion for a system's shape degrees of freedom from its evolution equations for
the $3N$ absolute configuration degrees of freedom, the Boltzman-Hamel
equations of motion in an non-holonomic frame on the tangent space $T(Q)$ to
the system's absolute configuration space $Q$ is adapted to the $Sim(3)$ fiber
bundle structure of the configuration space. The derived equations of motion on
shape space enable us, among other things, to predict the evolution of the
shape of a classical system governed by this theory without any reference to
its absolute position, orientation, or size in space. The paper will explain,
that by treating the measuring instruments as part of the matter in the theory,
how the mass metric $\textbf{M}$ on the configuration space $Q$ uniquely
defines a metric on the reduced tangent bundle $\frac{T(Q)}{Sim(3)}$, and how
the unique metric structure on shape space $S$ can be derived. After deriving
the reduced equations of motion on shape space for a general $N$-body system,
the shape equations of motion for a three-body system in suitable coordinates
is given as an illustration.
