@article{padgett_mazzoleni_faw_2015, title={Survey of shock wave structures of smooth particle granular flows}, volume={92}, ISSN={["1550-2376"]}, DOI={10.1103/physreve.92.062209}, abstractNote={We show the effects of simulated supersonic granular flow made up of smooth particles passing over two prototypical bodies: a wedge and a disk. We describe a way of computationally identifying shock wave locations in granular flows and tabulate the shock wave locations for flow over wedges and disks. We quantify the shock structure in terms of oblique shock angle for wedge impediments and shock standoff distance for disk impediments. We vary granular flow parameters including upstream volume fraction, average upstream velocity, granular temperature, and the collision coefficient of restitution. Both wedges and disks have been used in the aerospace community as prototypical impediments to flowing air in order to investigate the fundamentally different shock structures emanating from sharp and blunt bodies, and we present these results in order to increase the understanding of the fundamental behavior of supersonic granular flow.}, number={6}, journal={Physical Review E}, author={Padgett, D. A. and Mazzoleni, A.P. and Faw, Stormy D.}, year={2015}, month={Dec}, pages={062209} }
 @article{padgett_mazzoleni_2007, title={Analysis and design for no-spin tethered satellite retrieval}, volume={30}, ISSN={["0731-5090"]}, DOI={10.2514/1.25390}, abstractNote={T ETHERED satellites are composed of two or more orbiting bodies connected by light, flexible members known as tethers. The study of tethered satellites began with Tsilokovsky in 1895 and was taken up by Artsutanov in the 1950s [1]. Since that time a number of researchers have studied aspects of the application of tethered satellite systems including the dynamics of tethered satellites and the architecture of tethered satellite missions [1–9]. Tethered satellites are of interest both because of the physical and mathematical problems they present and because of their many practical uses. Tethered satellite systems have been identified as candidates for novel atmospheric probes, interferometers, magnetometers, and gravity gradiometers among other devices [10–14]. Some far term applications of tethered satellites include the tethered artificial gravity (TAG) system and the momentum exchange and electrodynamic reboost (MXER) system. The TAG system is a device capable of imparting an artificial gravitational force to bodies on orbit [15], whereas the MXER system is a momentum exchange device designed to boost payloads into higher orbits without the use of chemical propellants [16]. Numerous other uses for tethered satellites in space are detailed in [17]. During the course of a tethered satellite mission, it may be necessary to shorten the overall length of the tether. The purpose of such a retrieval could be to facilitate the repair or servicing of the tethered satellite assembly, to reduce the profile of the orbital debris created by a satellite at the end of its useful life, or simply to alter the dynamical behavior of the tethered satellite system. We will show that in general, such a length contraction causes the tethered satellite system to enter a spin with respect to the orbital reference frame. In many of the instances described above, the reason for retrieving a tethered satellite system necessitates that the system not spin with respect to the orbital reference frame; such a maneuver could be achieved through the use of a sophisticated angular velocity control system. However, by exploiting the dynamics of a tethered satellite system, it is possible to reduce the length of the system without causing the system to enter a spin. Analysis of the equations of motionwill reveal that under an exponential length control law, there exist initial tethered satellite states for which the tethered satellite system can be retrieved and remain stationary with respect to the orbital reference frame during the course of the retrieval maneuver. These points, which correspond to the equilibria of the system, will be identified and classified. We will describe the motion of a simplified tethered satellite system undergoing retrieval in the neighborhood of these equilibrium points.}, number={5}, journal={JOURNAL OF GUIDANCE CONTROL AND DYNAMICS}, author={Padgett, David A. and Mazzoleni, Andre P.}, year={2007}, pages={1516–1519} }
 @article{padgett_mazzoleni_2007, title={Nullcline analysis as an analytical tethered satellite mission design tool}, volume={30}, ISSN={["0731-5090"]}, DOI={10.2514/1.20946}, abstractNote={Tethered satellite systems have been proposed for many space mission applications due to the useful dynamics that can be generated with relatively low fuel expenditures. Increasing interest in tethered satellite systems necessitates a fundamental understanding of the dynamics of such systems. An analytic method of qualitatively describing the possible dynamics of a tethered satellite system is presented. This analysis is centered on the study of the sets of states for which at least one of the nondimensional time derivatives of the state variables is zero. These sets are known as the nullclines of a system, and they bound regions of the phase plane in which tethered satellite behavior is similar. The qualitative analysis of the nullclines provides an explanation for, and suggests the controllability of, many types of tethered satellite behavior. For the purposes of this paper, a tethered artificial gravity satellite system is used as a canonical tethered system and the results derived are applied to this system. The utility of the described analytical method is demonstrated by using the method to characterize two different tethered satellite missions.}, number={3}, journal={JOURNAL OF GUIDANCE CONTROL AND DYNAMICS}, author={Padgett, David A. and Mazzoleni, Andre P.}, year={2007}, pages={741–752} }
 @article{mantri_mazzoleni_padgett_2007, title={Parametric study of deployment of tethered satellite systems}, volume={44}, ISSN={["1533-6794"]}, DOI={10.2514/1.22955}, abstractNote={Deployment of a tethered satellite system is the process of separating the two end bodies by spooling out the tether connecting them. In this paper, we describe a 3-Dmodel of a tethered satellite system undergoing deployment. From the equations of motion obtained using the 3-D model, we identify five system parameters that affect the length to which a tethered satellite systemwill deploy. The equations ofmotion describing the tether deployment are solved for a given range of each of the parameters to determine the effect of each of the parameters on the level of deployment reached. The equations are then nondimensionalized; nondimensionalization reduces the number of system parameters fromfive to two and increases the generality of the equations ofmotion. The nondimensional equations of motion are solved numerically, and the results are presented in charts andplots that can be used bymission designers to predict the final deployed length under given operating conditions. Two case studies are presented to demonstrate the utility of these tools.}, number={2}, journal={JOURNAL OF SPACECRAFT AND ROCKETS}, author={Mantri, Parag and Mazzoleni, Andre P. and Padgett, David A.}, year={2007}, pages={412–424} }