Secular changes in the orbits of the quadruple system VW LMi

VW LMi is the tightest known quadruple system with 2 + 2 hierarchy. It consists of a W UMa-type eclipsing binary (P₁₂ = 0.477 55 d) and another detached non-eclipsing binary (P₃₄ = 7.93 d) orbiting around a common centre of mass in about P₁₂₃₄ = 355 d. We present new observations of the system extending the time baseline to study long-term perturbations in the system and to improve orbital elements. The multidataset modelling of the system (four radial-velocity curves for the components and the timing data) clearly showed an apsidal motion in the non-eclipsing binary at a rate of 4.6 deg yr^-1, but no other perturbations. This is consistent with the nearly co-planarity of the outer, 355-d orbit, and the 7.93-d orbit of the non-eclipsing binary. Extensive N-body simulations enabled us to constrain the mutual inclination of the non-eclipsing binary and the outer orbits to j_34-1234 < 10 deg.