Survey of highly non-Keplerian orbits with low-thrust propulsion

Celestial mechanics has traditionally been concerned with orbital motion under the action of a conservative gravitational potential. In particular, the inverse square gravitational force due to the potential of a uniform, spherical mass leads to a family of conic section orbits, as determined by Isaac Newton, who showed that Kepler‟s laws were derivable from his theory of gravitation. While orbital motion under the action of a conservative gravitational potential leads to an array of problems with often complex and interesting solutions, the addition of non-conservative forces offers new avenues of investigation. In particular, non-conservative forces lead to a rich diversity of problems associated with the existence, stability and control of families of highly non-Keplerian orbits generated by a gravitational potential and a non-conservative force. Highly non-Keplerian orbits can potentially have a broad range of practical applications across a number of different disciplines. This review aims to summarize the combined wealth of literature concerned with the dynamics, stability and control of highly non-Keplerian orbits for various low thrust propulsion devices, and to demonstrate some of these potential applications

Generalized packing designs

Generalized $t$-designs, which form a common generalization of objects such as $t$-designs, resolvable designs and orthogonal arrays, were defined by Cameron [P.J. Cameron, A generalisation of $t$-designs, \emph{Discrete Math.}\ {\bf 309} (2009), 4835--4842]. In this paper, we define a related class of combinatorial designs which simultaneously generalize packing designs and packing arrays. We describe the sometimes surprising connections which these generalized designs have with various known classes of combinatorial designs, including Howell designs, partial Latin squares and several classes of triple systems, and also concepts such as resolvability and block colouring of ordinary designs and packings, and orthogonal resolutions and colourings. Moreover, we derive bounds on the size of a generalized packing design and construct optimal generalized packings in certain cases. In particular, we provide methods for constructing maximum generalized packings with $t=2$ and block size $k=3$ or 4.Comment: 38 pages, 2 figures, 5 tables, 2 appendices. Presented at 23rd British Combinatorial Conference, July 201

HOPs and COPs: Room frames with partitionable transversals

In this paper, we construct Room frames with partitionable transversals. Direct and recursive constructions are used to find sets of disjoint complete ordered partitionable (COP) transversals and sets of disjoint holey ordered partitionable (HOP) transversals for Room frames. Our main results include upper and lower bounds on the number of disjoint COP transversals and the number of disjoint HOP transversals for Room frames of type 2n. This work is motivated by the large number of applications of these designs

Wake Structures and Surface Patterns of the DrivAer Notchback Car Model under Side Wind Conditions

The flow field topology of passenger cars considerably changes under side wind conditions. This changes the surface pressure, aerodynamic force, and drag and performance of a vehicle. In this study, the flow field of a generic passenger vehicle is investigated based on three different side wind angles. The study aimed to identify vortical structures causing changes in the rear pressure distribution. The notchback section of the DrivAer model is evaluated on a scale of 1:4. The wind tunnel tests are conducted in a closed section with a splitter plate at a Reynolds number of 3 million. The side wind angles are 0∘ , 5∘ , and 10∘ . The three-dimensional and time-averaged flow field downstream direction of the model is captured by a stereoscopic particle image velocimetry system performed at several measurement planes. These flow field data are complemented by surface flow visualizations performed on the entire model. The combined approaches provide a comprehensive insight into the flow field at the frontal and side wind inflows. The flow without side wind is almost symmetrical. Longitudinal vortices are evident along the downstream direction of the A-pillar, the C-pillars, the middle part of the rear window, and the base surface. In addition, there is a ring vortex downstream of the vehicle base. The side wind completely changes the flow field. The asymmetric topology is dominated by the windward C-pillar vortex, the leeward A-pillar vortex, and other base vortices. Based on the location of the vortices and the pressure distributions measured in earlier studies, it can be concluded that the vortices identified in the wake are responsible for the local minima of pressure, increasing the vehicle drag