STA, the Space Trajectory Analysis Project

This article describes the objectives of the Space Trajectory Analysis (STA) project. The article also details the birth of STA, and its present configuration. STA is a project to develop an open source astrodynamics software suite involving university science departments and space research institutions. It was initiated by ESA as internal activity in 2005 and now it involves 16 partners. The article explains the partnership into the STA Steering Board. The main purpose of the STA is to allow advanced simulation for the analysis of space trajectories in an open and free environment under the premises of innovation and reliability.Further, the article explains that the STA development is open source and is based on the state of the art astrodynamics routines that are grouped into modules. Finally, the article concludes about the benefits of the STA initiative: the STA project allows a strong link among applied mathematics, space engineering, and informatics disciplines by reinforcing the academic community with requirements and needs coming from real missions

MPCC: Critical Point Theory

We study mathematical programs with complementarity constraints (MPCC) from a topological point of view. Special focus will be on C-stationary points. Under the Linear Independence Constraint Qualification (LICQ) we derive an equivariant Morse Lemma at nondegenerate C-stationary points. Then, two basic theorems from Morse Theory (deformation theorem and cell-attachment theorem) are proved. Outside the C-stationary point set, continuous deformation of lower level sets can be performed. As a consequence, the topological data (such as the number of connected components) then remain invariant. However, when passing a C-stationary level, the topology of the lower level set changes via the attachment of a q-dimensional cell. The dimension q equals the stationary C-index of the (nondegenerate) C-stationary point. The stationary C-index depends on both the restricted Hessian of the Lagrangian and the Lagrange multipliers related to bi-active complementarity constraints. Finally, some relations with other stationarity concepts, such as W-, A-, M-, S- and B-stationarity, are discussed