We compare several systems of equations in multiple dynamical cores, to study their applicability to a spectrum of atmospheric scales from cloud-resolving to planetary scales. The systems of equations include fully compressible, anelastic, and unified. The quasi-hydrostatic system is also included when relevant. The dynamical cores differ by prediction of momentum, the vertical component of the vorticity and the divergence of the horizontal wind, or three-dimensional vorticity. We will present simulations of stratospheric gravity waves excited by the impact of a warm-bubble with the tropopause. We will also present simulations of extratropical cyclones and ultra-long planetary waves in a beta-plane channel.