Cristina Stoica Department of Mathematics and Statistics, University of Surrey, U.K. Relative equilibria in mechanical systems with isotropy Wednesday 18th, August 14:05-14:55pm, Carslaw Lecture Theatre 273. Given a mechanical system with a symmetry group acting on it, symmetric points in configuration space are points with non-trivial isotropy subgroups. Generally, at this points, the reduced space is not a manifold. Using a version of the slice theorem and given a Lagrangian function, we offer a constructive method to compute the equations of motion and the relative equilibria conditions in a model space based at a symmetric point. We compare our results with previous developments and apply them to simple mechanical systems. This work is joint with Mark Roberts (Surrey) and Tanya Schmah (Macquarie).