Applications of variational methods to some three-point boundary value problems with instantaneous and noninstantaneous impulses

In this paper, we study the multiple solutions for some second-order p-Laplace differential equations with three-point boundary conditions and instantaneous and noninstantaneous impulses. By applying the variational method and critical point theory the multiple solutions are obtained in a Sobolev space. Compared with other local boundary value problems, the three-point boundary value problem is less studied by variational method due to its variational structure. Finally, two examples are given to illustrate the results of multiplicity

Astronautics

Many people have had and still have misconceptions about the basic principle of rocket propulsion. Here is a comment of an unknown editorial writer of the renowned New York Times from January 13, 1920, about the pioneer of US astronautics, Robert Goddard, who at that time was carrying out the ?rst experiments with liquid propulsion engines: Professor Goddard … does not know the relation of action to reaction, and of the need to have something better than a vacuum against which to react – to say that would be absurd. Of course he only seems to lack the knowledge ladled out daily in high schools

Optimal orbital transfer using a Legendre pseudospectral method

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2003.Includes bibliographical references (p. 155-158).by Stuart Andrew Stanton.S.M

Low Thrust Trajectories in Multi Body Regimes

More and more stringent and unique mission requirements motivate to exploring solutions, already in the preliminary mission analysis phase, going far beyond the classical chemical-Keplerian approach. The present dissertation deals with the analysis and the design of highly non linear orbits arising both from the inclusion of different gravitational sources in the dynamical models, and from the use of electric system for primary propulsion purposes. The equilibrium of different gravitational fields, on one hand, permits unique transfer solutions and operational orbits, on the other hand, the high thrust efficiency, characteristic of an electric device, reduces the propellant mass required to accomplish the transfer. Each of these models, and even better their combination, enables trajectories able to satisfy mission requirements not otherwise met, first of all to reduce the propellant mass fraction of a given mission. The inclusion of trajectory arcs powered by an electric thruster, providing a low thrust for extended duration, makes essential the use of optimal control theory in order to govern the thrust law and thus design the required transfers so as to minimizing/maximizing specific indexes. The goal is, firstly, to review the possible advantages and the main limits of dynamical models and, afterward, to define methodologies to preliminary design non-Keplerian missions both in interplanetary contexts and in the Earth-Moon system. Special emphasis is given to the study of dynamical systems through which the main features of the Circular Restricted Three Body Model (the first one among the non-Keplerian models) can be identified, implemented and used. Purely ballistic solutions enabled by this model are first independently explored and after considered as target orbits for electric thrusting phases. Electric powered arcs are used to link ballistic phases arising from the balancing of different gravitational influences. This concept is applied both for the exploration of planetary regions and for interplanetary transfer purposes. Together with low thrust missions to selenocentric orbits designed taking into account both the Earth and the Moon gravity, also transfer solutions toward periodic orbits moving in the Earth-Moon region are presented. These are designed considering electric thrusting arcs and ballistic segments exploring for free specific space regions. In brief, theoretical models deriving from dynamical system theory and from optimal control theory are employed to design non conventional orbits in non linear astrodynamics models

Periodic Orbits in the Circular restricted Three-Body Problem and Transfers from the Lunar Gateway to Lunar Repeating Ground Track Orbits

This thesis explores the use of periodic orbits in the Earth-Moon Circular Restricted Three-Body Problem (CR3BP) for lunar mission design. First a number of families of periodic orbits, e.g. Lyapunov, Halo, Vertical, Distant Retrograde Orbit (DRO) families, are computed using differential correction techniques. The stability properties, and the presence of bifurcations along these families of orbits are studied in detail. Then we explore the use of invariant manifolds to compute heteroclinic and homoclinic transfers between L_1 and L_2 Lyapunov orbits. Finally we extend the CR3BP model by including the lunar gravitational field. We show how to compute families of lunar Repeating Ground Track (RGT) orbits at different altitudes and inclinations, and explore possible transfers between the Lunar Gateway and lunar RGT orbits.This thesis explores the use of periodic orbits in the Earth-Moon Circular Restricted Three-Body Problem (CR3BP) for lunar mission design. First a number of families of periodic orbits, e.g. Lyapunov, Halo, Vertical, Distant Retrograde Orbit (DRO) families, are computed using differential correction techniques. The stability properties, and the presence of bifurcations along these families of orbits are studied in detail. Then we explore the use of invariant manifolds to compute heteroclinic and homoclinic transfers between L_1 and L_2 Lyapunov orbits. Finally we extend the CR3BP model by including the lunar gravitational field. We show how to compute families of lunar Repeating Ground Track (RGT) orbits at different altitudes and inclinations, and explore possible transfers between the Lunar Gateway and lunar RGT orbits

Natural and artificial orbits around the Martian moon Phobos

One of the paramount stepping stones towards the long-term goal of undertaking human missions to Mars is the exploration of the Martian moons. In particular, Phobos is becoming an appealing destination for future scientific missions of NASA and ESA. Phobos is a tiny celestial body that orbits around Mars at low altitude. The unique combination of these two characteristics yields the sphere of influence of the moon to be very close to its surface. Therefore, orbital dynamics around Phobos are particularly complex, because many strong perturbations are involved. The classical models of the Keplerian two-body problem, and the circular three-body problem are not accurate enough to describe the motion of a spacecraft in the vicinity of Phobos. In this thesis, the description of the relative orbital dynamics in proximity of this moon is extended to a more accurate nonlinear model. This is undertaken by the inclusion of the perturbations due to the orbital eccentricity and the inhomogeneous gravity field of Phobos. Subsequently, several classes of non-Keplerian orbits are identified, using the analytical and numerical methodologies of dynamical systems theory. These techniques exploit the improved description of the natural dynamics, enabled by the extended model, to provide low-cost guidance trajectories, that minimize the fuel consumption and extend the mission range. In addition, the potential of exploiting artificial orbits with lowthrust is investigated. The performance and requirements of these orbits are assessed, and a number of potential mission applications near Phobos are proposed. These low-cost operations include close-range observation, communication, passive radiation shielding, and orbital pitstops for human space flight. These results could be exploited in upcoming missions targeting the exploration of this Martian moon. Furthermore, the new model can provide evidence to support the accretion theory of Phobos' origin, and to explain the formation of the craters and grooves on Phobos

Leveraging Manifold Theory for Trajectory Design - A Focus on Futuristic Cislunar Missions

Optimal control methods for designing trajectories have been studied extensively by astro-dynamicists. Direct and indirect methods provide separate approaches to arrive at the optimal solution, each having their associated advantages and challenges. Among the realm of optimized transfer trajectories, fuel-optimal trajectories are typically most sought and characterized by se-quential thrust and coast arcs. On the other hand, it is well known that a simplified dynamical model like the CR3BP analyzed in a rotating coordinate system, reveal fixed points known as Lagrange points. These spatial points can be orbited, with researchers categorizing periodic orbits around them starting from the simple planar Lyapunov orbits and continuing to the more enigmatic butterfly orbits. Studying linearized dynamics using eigenanalysis in the vicinity of a point on these periodic orbits lead to interesting departures spatially manifesting into the invariant manifolds. This thesis delves into the novel idea of merging aspects of invariant manifold theory and indirect optimal control methods to provide efficient computation of feasible transfer trajectories. The marriage of these ideas provide the possibility of alleviating the challenges of an end-to end optimization using indirect methods for a long mission by utilizing the pre-computed and analyzed manifolds for insertion points of a long terminal coast arc. In addition to this, realistic and accurate mission scenarios require consideration of a high-fidelity dynamical model as well as shadow constraints. A methodology to use the “manifold analogues” in such cases has been discussed and utilized in this thesis along with modelling of eclipses during optimization, providing mission designers a basis for efficient and accurate/mission-ready trajectory design. This overcomes the shortcomings in state of the art software packages such as MYSTIC and COPERNICUS

Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015

This volume contains the full papers accepted for presentation at the ECCOMAS Thematic Conference on Multibody Dynamics 2015 held in the Barcelona School of Industrial Engineering, Universitat Politècnica de Catalunya, on June 29 - July 2, 2015. The ECCOMAS Thematic Conference on Multibody Dynamics is an international meeting held once every two years in a European country. Continuing the very successful series of past conferences that have been organized in Lisbon (2003), Madrid (2005), Milan (2007), Warsaw (2009), Brussels (2011) and Zagreb (2013); this edition will once again serve as a meeting point for the international researchers, scientists and experts from academia, research laboratories and industry working in the area of multibody dynamics. Applications are related to many fields of contemporary engineering, such as vehicle and railway systems, aeronautical and space vehicles, robotic manipulators, mechatronic and autonomous systems, smart structures, biomechanical systems and nanotechnologies. The topics of the conference include, but are not restricted to: ● Formulations and Numerical Methods ● Efficient Methods and Real-Time Applications ● Flexible Multibody Dynamics ● Contact Dynamics and Constraints ● Multiphysics and Coupled Problems ● Control and Optimization ● Software Development and Computer Technology ● Aerospace and Maritime Applications ● Biomechanics ● Railroad Vehicle Dynamics ● Road Vehicle Dynamics ● Robotics ● Benchmark ProblemsPostprint (published version