Normalization and reduction of the Stark Hamiltonian

Abstract

We detail a calculation of the second order normal form of the Stark effect Hamiltonian after regularization, using the Kustaanheimo-Stiefel mapping. After reduction, we obtain an integrable two degree of freedom system on $ S^2_h \times S^2_h $, which we reduce again to obtain a one degree of freedom Hamiltonian system.