Compact synchrotrons, such as the HeLICS ring proposed by the NIMMS collaboration for cancer therapy and research, use short and strongly curved dipoles. In some cases, these dipoles are designed as combined-function magnets, for example to maintain beam stability within the dipoles or to make the machine more compact. Such large curvature magnets introduce non-linear effects that may limit the dynamic aperture. As in the case of straight magnets, an appropriate parametrisation of the magnetic field in a suitable reference frame is required to capture the relevant long-term dynamical effects. In this seminar, I present a framework that links field specifications to beam dynamics requirements, enabling the derivation of resonance driving terms and the estimation of relevant beam parameters, and providing a consistent basis for design expectations.