  Shape Dynamics is a theory of gravity that waives refoliation invariance in
favor of spatial Weyl invariance. It is a canonical theory, constructed from a
Hamiltonian, 3+1 perspective. One of the main deficits of Shape Dynamics is
that its Hamiltonian is only implicitly constructed as a functional of the
phase space variables. In this paper, I write down the equations of motion for
Shape Dynamics to show that over a curve in phase space representing a
Minkowski spacetime, Shape Dynamics possesses Poincar\'e symmetry for
appropriate boundary conditions. The proper treatment of such boundary
conditions leads us to completely formulate Shape Dynamics for open manifolds
in the asymptotically flat case. We study the charges arising in this case and
find a new definition of total energy, which is completely invariant under
spatial Weyl transformations close to the boundary. We then use the equations
of motion once again to find a non-trivial solution of Shape Dynamics,
consisting of a flat static Universe with a point-like mass at the center. We
calculate its energy through the new formula and rederive the usual
Schwarzschild mass.
