Gravitational wave solutions of quadratic curvature gravity using a null coframe formulation

Quadratic curvature gravity equations are projected to a complex null coframe by using the algebra of exterior forms and expressed in terms of the spinor quantities defined originally by Newman and Penrose. As an application, a new family of impulsive gravitational wave solutions propagating in various type D backgrounds is introduced.Comment: Title rephrased, minor changes in the text. Conclusion expanded and new references adde

Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems

The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this problem class. Recent numerical methods for nonsmooth dynamical systems subject to unilateral contact and friction illustrate the topicality of this development.Comment: Preprint of Book Chapte

Bayesian Estimation for Continuous-Time Sparse Stochastic Processes

We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By relying on tools from the theory of splines, we derive the joint a priori distribution of the samples and show how this probability density function can be factorized. The factorization enables us to tractably implement the maximum a posteriori and minimum mean-square error (MMSE) criteria as two statistical approaches for estimating the unknowns. We compare the derived statistical methods with well-known techniques for the recovery of sparse signals, such as the $\ell_1$ norm and Log ($\ell_1$-$\ell_0$ relaxation) regularization methods. The simulation results show that, under certain conditions, the performance of the regularization techniques can be very close to that of the MMSE estimator.Comment: To appear in IEEE TS

Incorporation of Mission Design Constraints in Floquet Mode and Hamiltonian Structure-Preserving Orbital Maintenance Control Strategies for Libration Point Orbits

Libration point orbits are, in general, inherently unstable. Without the presence of corrective maneuvers a spacecraft will diverge from the vicinity of such trajectories. In this research effort, two orbital maintenance control strategies are studied: the impulsive Floquet Mode (FM) controller and the continuous Hamiltonian Structure-Preserving (HSP) controller. These two controllers are further developed to incorporate real-world mission design constraints. The FM controller is modified to accommodate feasible maneuver directions that are constrained to a plane or a line. This controller is shown to be applicable for orbital station-keeping of spin stabilized spacecraft that are only equipped with either tangential thrusters or axial thrusters. The HSP controller is extended for application to general three-dimensional hyperbolic libration point orbits, and then discretized to account for the minimum time required for orbit determination and/or scientific operations. Both controllers are applied to an unstable 1 halo orbit in the Sun-Earth/Moon system. The performances of these controllers are examined under the impacts of the spacecraft’s operation errors and mission design constraints. Simulation results suggest that the FM controller is capable of maintaining the motion of the spacecraft in the vicinity of the desired reference trajectory for the duration of the simulation, while satisfying all mission design constraints. The discrete-time MHSP controller proves to be able to improve the stability of the nominal trajectory by reducing the value of the unstable Poincare exponent of the reference orbit

Existence of three solutions for impulsive multi-point boundary value problems

This paper is devoted to the study of the existence of at least three classical solutions for a second-order multi-point boundary value problem with impulsive effects. We use variational methods for smooth functionals defined on reflexive Banach spaces in order to achieve our results. Also by presenting an example, we ensure the applicability of our results

Guidance, flight mechanics and trajectory optimization. Volume 12 - Relative motion, guidance equations for terminal rendezvous

Equations of relative motion and guidance for orbital transfer and docking maneuvers in spacecraft rendezvou