  In analogy to the harmonic analysis for the Poincar\'e group with its
irreducible representations characterizing free particles, the harmonic
analysis for a nonlinear spacetime model as homogenous space of the extended
Lorentz group GL(C^2) is given. What the Dirac energy-momentum measures are for
free particles, are multipole measures in the analysis of nonlinear spacetime -
they are related to spacetime interactions. The representations induced from
the nonlinear spacetime fixgroup U(2) connect representations of external
(spacetimelike) degrees of freedom with those of internal
(hypercharge-isospinlike) ones as seen in the standard model of electroweak and
strong interactions. The methods used are introduced and exemplified with the
nonrelativistic Kepler dynamics in an interpretation as harmonic analysis of
time and position functions.
