No abstract

In this article, we introduce a novel three-step approach for solving optimal control problems in space mission design. We demonstrate its potential by the example task of sending a group of spacecraft to a specific Earth L 2 halo orbit. In each of the three steps we make use of recently developed optimization methods and the result of one step serves as input data for the subsequent one. Firstly, we perform a global and multi-objective optimization on a restricted class of control functions. The solutions of this problem are (Pareto-)optimal with respect to V and flight time. Based on the solution set, a compromise trajectory can be chosen suited to the mission goals. In the second step, this selected trajectory serves as initial guess for a direct local optimization. We construct a trajectory using a more flexible control law and, hence, the obtained solutions are improved with respect to control effort. Finally, we consider the improved result as a reference trajectory for a formation flight task and compute trajectories for several spacecraft such that these arrive at the halo orbit in a prescribed relative configuration. The strong points of our three-step approach are that the 123 34 M. Dellnitz et al.challenging design of good initial guesses is handled numerically by the global optimization tool and afterwards, the last two steps only have to be performed for one reference trajectory.

Recently new techniques for the design of energy efficient trajectories for space missions have been proposed that are based on the circular restricted three body problem as the underlying mathematical model. These techniques exploit the structure and geometry of certain invariant sets and associated invariant manifolds in phase space to systematically construct energy efficient flight paths. In this paper, we extend this model in order to account for a continuously applied control force on the spacecraft as realized by certain low thrust propulsion systems. We show how the techniques for the trajectory design can be suitably augmented and compute approximations to trajectories for a mission to Venus.

During the last decade set oriented methods have been developed for the approximation and analysis of complicated dynamical behavior. These techniques do not only allow the computation of invariant sets such as attractors or invariant manifolds. Also statistical quantities of the dynamics such as invariant measures, transition probabilities, or (finite-time) Lyapunov exponents, can be efficiently approximated. All these techniques have natural applications in the numerical treatment of problems in astrodynamics. In this contribution we will give an overview of the set oriented numerical methods and how they are successfully used for the solution of astrodynamical tasks. For the demonstration of our results we consider the (planar) circular restricted three body problem. In particular, we approximate invariant manifolds of periodic orbits about the L 1 and L 2 equilibrium points and show an extension to the application of a continuous control force. Moreover, we demonstrate that expansion rates (finite-time Lyapunov exponents), which so far have mainly been applied in fluid dynamics, can provide useful information on the qualitative behavior of trajectories in the context of astrodynamics. The set oriented numerical methods and their application to astrodynamical problems discussed in this contribution serve as further important steps towards understanding the pathways of comets or asteroids and the design of energy-efficient trajectories for spacecraft.

In Germany, orthopedic and trauma surgery rank first in the number of alleged malpractice claims amongst all medical disciplines. Thus, the German Association of Trauma and Orthopedic Surgery, together with the Bavarian Chamber of Physicians, set out to identify potential predictors of approved malpractice claims to improve process quality. In a case-control study, 164 cases of approved malpractice claims were matched according to age and gender to 336 controls of rejected claims, based on the 2004 to 2006 dataset of the Bavarian Chamber of Physicians. Potential predictors of acceptance of an alleged incident were modeled by uni- and multivariate logistic regression analysis. The final model explained 71% of the probability of acceptance of an asserted claim. It contained three medical consequences (i.e. delayed healing, reoperation, and loss of motion), one specific entity (i.e. fracture) and one socio-demographic variable (i.e. professional driver) as independent predictors of acceptance. Insufficient or lacking explanation of the planned procedure to patients or relatives and / or lacking informed consent (odds ratio [OR] 2.33, 95% confidence interval [CI]1.23-4.43), as well as inappropriate, low-quality, or erroneously interpreted imaging (OR 1.90, 95% CI 1.06-3.41) independently contributed to the likelihood of acceptance of a legal claim. Strict adherence to the principles of surgical quality assurance in terms of transparent patient information and joint informed consent procedures, as well as intransigent radiological imaging are mandatory to foster surgeon-patients-relationships and to avoid later legal claims.