  A bar-joint framework $(G,p)$ in a (non-Euclidean) real normed plane $X$ is
the combination of a finite, simple graph $G$ and a placement $p$ of the
vertices in $X$. A framework $(G,p)$ is globally rigid in $X$ if every other
framework $(G,q)$ in $X$ with the same edge lengths as $(G,p)$ arises from an
isometry of $X$. The weaker property of local rigidity in normed planes (where
only $(G,q)$ within a neighbourhood of $(G,p)$ are considered) has been studied
by several researchers over the last 5 years after being introduced by Kitson
and Power for $\ell_p$-norms. However global rigidity is an unexplored area for
general normed spaces, despite being intensely studied in the Euclidean context
by many groups over the last 40 years. In order to understand global rigidity
in $X$, we introduce new generalised rigid body motions in normed planes where
the norm is determined by an analytic function. This theory allows us to deduce
several geometric and combinatorial results concerning the global rigidity of
bar-joint frameworks in $X$.
