@article{hartl_miller_mazzoleni_2013, title={Dynamics of a dissipative, inelastic gravitational billiard}, volume={87}, ISSN={["1550-2376"]}, DOI={10.1103/physreve.87.032901}, abstractNote={The seminal physical model for investigating formulations of nonlinear dynamics is the billiard. Gravitational billiards provide an experimentally accessible arena for their investigation. We present a mathematical model that captures the essential dynamics required for describing the motion of a realistic billiard for arbitrary boundaries, where we include rotational effects and additional forms of energy dissipation. Simulations of the model are applied to parabolic, wedge and hyperbolic billiards that are driven sinusoidally. The simulations demonstrate that the parabola has stable, periodic motion, while the wedge and hyperbola (at high driving frequencies) appear chaotic. The hyperbola, at low driving frequencies, behaves similarly to the parabola; i.e., has regular motion. Direct comparisons are made between the model’s predictions and previously published experimental data. The representation of the coefficient of restitution employed in the model resulted in good agreement with the experimental data for all boundary shapes investigated. It is shown that the data can be successfully modeled with a simple set of parameters without an assumption of exotic energy dependence.}, number={3}, journal={PHYSICAL REVIEW E}, author={Hartl, Alexandre E. and Miller, Bruce N. and Mazzoleni, Andre P.}, year={2013}, month={Mar} }
 @article{hartl_mazzoleni_2012, title={Terrain modeling and simulation of a tumbleweed rover traversing martian rock fields}, volume={49}, DOI={10.2514/1.57903}, abstractNote={Covers advancements in spacecraft and tactical and strategic missile systems, including subsystem design and application, mission design and analysis, materials and structures, developments in space sciences, space processing and manufacturing, space operations, and applications of space technologies to other fields.}, number={2}, journal={Journal of Spacecraft and Rockets}, author={Hartl, A. E. and Mazzoleni, A. P.}, year={2012}, pages={401–412} }
 @article{hartl_miller_mazzoleni_2011, title={Dynamic modeling and simulation of a real world billiard}, volume={375}, ISSN={["1873-2429"]}, DOI={10.1016/j.physleta.2011.08.038}, abstractNote={Gravitational billiards provide an experimentally accessible arena for testing formulations of nonlinear dynamics. We present a mathematical model that captures the essential dynamics required for describing the motion of a realistic billiard for arbitrary boundaries. Simulations of the model are applied to parabolic, wedge and hyperbolic billiards that are driven sinusoidally. Direct comparisons are made between the modelʼs predictions and previously published experimental data. It is shown that the data can be successfully modeled with a simple set of parameters without an assumption of exotic energy dependence.}, number={42}, journal={PHYSICS LETTERS A}, author={Hartl, Alexandre E. and Miller, Bruce N. and Mazzoleni, Andre P.}, year={2011}, month={Oct}, pages={3682–3686} }
 @article{hartl_mazzoleni_2010, title={Dynamic Modeling of a Wind-Driven Tumbleweed Rover Including Atmospheric Effects}, volume={47}, ISSN={["0022-4650"]}, DOI={10.2514/1.45174}, abstractNote={A tumbleweed rover is a spherical wind-driven rover designed to explore places of geological interest on the Martian surface. Dynamic models developed for an individual rover are used to create numerical simulations for a rover traversing through flat terrain, a channel, and a crater. The simulations show that the rover’s motion is dependent on the terrain type and initial and atmospheric conditions. The results confirm that the wind force both pushes and hinders the rover’s motion while sliding, rolling, and bouncing. The rover periodically transitions between these modes of movement when contact is initiated against sloped portions of terrain. Combinations of rolling and bouncing may be a more effective means of transport for a rover traveling through a channel when compared to rolling alone. The aerodynamic effects of drag and the Magnus force are contributing factors to the possible capture of the rover by a crater.}, number={3}, journal={JOURNAL OF SPACECRAFT AND ROCKETS}, author={Hartl, Alexandre E. and Mazzoleni, Andre P.}, year={2010}, pages={493–502} }
 @article{hartl_mazzoleni_2008, title={Parametric study of spherical rovers crossing a valley}, volume={31}, ISSN={["0731-5090"]}, DOI={10.2514/1.33932}, abstractNote={T HE evidence ofwater onMars and the idea of using themoon as a staging ground for future planetary missions has increased interest in Martian and lunar exploration. Future missions will require the exploration of large areas on these surfaces because areas of scientific interest may be far away from the landing sites. Because of the inherent dangers with manned missions, rovers provide a viable option for future investigations of these regions. NASA currently employs wheeled rovers, including the Mars exploration rovers, to examine the Martian surface. These rovers are intricate and expensive, with limited ability to navigate rough terrain. This complicates gathering scientific data on Martian climate and geology and renders answering questions on the existence of water and life difficult. A vehicle capable of exploring large areas of terrain is the tumbleweed rover. A tumbleweed is a spherical (wind driven or selfpropelled) rover designed to provide superior mobility and greater accessibility on the surface of Mars and the moon. Compared with conventional wheeled rovers, a tumbleweed can cover vast distances faster and reach previously inaccessible areas of scientific interest, such as canyons and valleys. Because a tumbleweed is significantly less expensive than traditional rovers, multiple tumbleweeds can be deployed across the Martian or lunar surface for scientific surveys. The tumbleweed’s design is also well suited for polar missions because the rover can seek out water sources beneath a surface desert or an ice sheet, a task that cannot be done accurately from orbit. For these reasons, parametric studies describing and predicting a tumbleweed’s motion across the Martian or lunar terrain is valuable. The tumbleweed rover is based on concepts going back to the 1970s, where Jacques Blamont of the National Center for Space Studies developed the notion for wind-driven rovers. The concept has been pursued by several investigators at the NASA Langley Research Center (LaRC) and at the Jet Propulsion Laboratory (JPL). LaRC is focusing on concepts based on lightweight deployable structures, while JPL is focusing on inflatable concepts based on airbag landing technology. Other organizations, including Texas Technical University (TTU), North Carolina State University (NCSU), and the Swiss Federal Institute of Technology, are also examining wind-driven rover concepts. Research into the tumbleweed rover’s dynamics, however, is in its early stages. Feasibility studies on wind-driven mobility on the surface of Mars have been examined [1–8] and other studies have presented dynamic models for particular tumbleweed concepts [9– 14]. Several areas have been identified where the existing research can be expanded. Particularly, a numerical simulation model predicting a tumbleweed’s motion for arbitrary terrains is needed. Also required are parametric studies describing the tumbleweed’s behaviors on these terrains, which include flat planes, hills, ravines, and valleys. This paper presents parametric studies of a tumbleweed (or spherical) rover as it moves across a valley. The model used covers the rover’s bouncing, sliding, and rolling behaviors and its transitions between different terrain types. We present studies of the rover’s motion for various sets of parameters and initial conditions. Theses parametric studies will provide an understanding of the range of tumbleweed design parameters essential for mobility over shallow and deep valleys on Mars.}, number={3}, journal={JOURNAL OF GUIDANCE CONTROL AND DYNAMICS}, author={Hartl, Alexandre E. and Mazzoleni, Andre P.}, year={2008}, pages={775–779} }