Kaasalainen's research interests mostly focused on mathematical modelling in various fields ranging from
remote sensing and space research to planetary and galactic dynamics. Typically, the models and mathematical methods Kaasalainen developed with his colleagues are connected with inverse problems. Two such topics featured prominently in Kaasalainen's research: • Asteroid
lightcurve inversion, i.e., the reconstruction of the shapes and spin states of
asteroids from their brightness measurements (
lightcurves), based on mathematical results and uniqueness and stability theorems that have been transformed into modelling algorithms with which a multitude of otherwise unresolvable asteroids can now be mapped. This method has also been used in the direct verification of the
Yarkovsky–O'Keefe–Radzievskii–Paddack effect in the
Solar System. • Analysis of large dynamical systems, where
torus construction methods in phase space allow a compact representation or approximation of the dynamics of the observed system (such as a
galaxy). ==References==