  We investigate integrable 2-dimensional Hamiltonian systems with scalar and
vector potentials, admitting second invariants which are linear or quadratic in
the momenta. In the case of a linear second invariant, we provide some examples
of weakly-integrable systems. In the case of a quadratic second invariant, we
recover the classical strongly-integrable systems in Cartesian and polar
coordinates and provide some new examples of integrable systems in parabolic
and elliptical coordinates.
