Andre P. Mazzoleni

Nonlinear Spacecraft Dynamics with a Flexible Appendage, Damping, and Moving Internal Submasses

We study the attitude dynamics of a single-body spacecraft that is perturbed by the motion of small oscillating submasses, a small e exible appendage constrained to undergo only torsional vibration, and a rotor immersed in a viscous e uid. We are interested in the chaotic dynamics that can occur for certain sets of the physical parameter values of the spacecraft when energy dissipation acts to drive the body from minor to major axis spin. Energy dissipation, which is present in all spacecraft systems and is the mechanism that drives the minor to major axis transition, is implemented via the rotor. We not only obtain an analytical test for chaos in terms of satellite parametersusing Melnikov’ s method, but wealso use extensivenumericalsimulation to check the rangeof validity of the Melnikov result.

Parametric Study of Deployment of Tethered Satellite Systems

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.

Asteroid Diversion Using Long Tether and Ballast

The threat of an asteroid or comet impacting the Earth has been receiving more attention in recent years, due in part to the discovery of the Apophis asteroid, which was at one time projected to have a significant probability of impacting the Earth in the year 2029. Although a later analysis of the Apophis trajectory precluded this impact, the threat has brought a lot of attention to the dangers posed by asteroids. Many ideas have been put forward for mitigating such threats. This paper presents one such technique: the attachment of a long tether and ballast mass to change the orbit of an Earth-threatening asteroid or comet. Specifically, for this paper, a parametric study was conducted to determine to what degree the trajectory of an asteroid or comet could be altered by attaching a tether and ballast for various values of orbital semimajor axis and eccentricity and for various tether lengths and ballast mass sizes. The results show that a long tether and ballast mass could be effective for such a diversion. It was found that the technique was most effective using longer tethers and larger ballast masses on asteroids or comets with smaller, more eccentric, orbits.

Analytical Criterion for Chaotic Dynamics in Flexible Satellites with Nonlinear Controller Damping

In this work, we study the attitude dynamics of a single body spacecraft that is perturbed by the motion of a small flexible appendage constrained to undergo only torsional vibration. In particular, we are interested in the chaotic dynamics that can occur for certain sets of the physical parameter values of the spacecraft when energy dissipation acts to drive the body from minor to major axis spin. Energy dissipation, which is present in all spacecraft systems and is the mechanism that drives the minor to major axis transition, is implemented by a quantitative energy sink that is modeled with a nonlinear controller. We obtain an analytical test for chaos in terms of satellite parameters by Melnikovs method. This analytical criterion provides a useful design tool to spacecraft engineers who are concerned with avoiding potentially problematic chaotic dynamics in their systems. In addition, we show that a spacecraft with a control system designed to provide energy dissipation can exhibit chaos because of the inherent flexibility of its components.

Design, Analysis and Testing of Mars Tumbleweed Rover Concepts

A Mars Tumbleweed rover is a spherical, wind-driven, planetary rover. Compared with conventional rovers, a tumbleweed rover can travel farther faster and gain access to areas such as valleys and chasms that previously were inaccessible. This paper presents design, mathematical modeling, computer simulation, and testing of various tumbleweed rover concepts. In particular, we present wind-tunnel data indicating that a box-kite configuration represents a promising tumbleweed rover design, we show that a working box-kite–type tumbleweed can be constructed, and we show that center of mass variation shows promise as the basis of a tumbleweed rover navigation system.

Conceptual design of ocean compressed air energy storage system

In this paper, an ocean compressed air energy storage (OCAES) system is introduced as a utility scale energy storage option for electricity generated by wind, ocean currents, tides, and waves off the coast of North Carolina. Geographically, a location from 40km to 70km off the coast of Cape Hatteras is shown to be a good location for an OCAES system. Based on existing compressed air energy storage (CAES) system designs, a conceptual design of an OCAES system with thermal energy storage (TES) is presented. A simple thermodynamic analysis is presented for an adiabatic CAES system which shows that the overall efficiency is 65.9%. In addition, finite element simulations are presented which show the flow induced loads which will be experienced by OCAES air containers on the ocean floor. We discuss the fact that the combination of the buoyancy force and the flow induced lift forces (due to ocean currents) generates a periodic loading on the storage container and seabed, and how this presents engineering challenges related to the development of adequate anchoring systems. We also present a system, based on hydrolysis, which can be used for storing energy (in the form of oxygen and hydrogen gas) in containers on the ocean floor.

Dynamic Modeling of a Wind-Driven Tumbleweed Rover Including Atmospheric Effects

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.

Analysis and optimization of a quasi-isothermal compression and expansion cycle for ocean compressed air energy storage (OCAES)

A numerical analysis of a quasi-isothermal thermodynamic cycle was undertaken for its application in an underwater energy storage system. The conceptual basis for the quasi-isothermal process is firstly a use of water pistons, as opposed to air or other gas medium, which improve heat transfer rate and minimize the temperature variation on both compression and expansion sides of the cycle and secondly a use of mechanical design that maximizes a surface area of heat transfer. Numerical analysis of the heat transfer cycle confirms the validity of the quasi-isothermal nature of the water pistons. Design factors such as surface area, stroke displacement, and frequency of piston action can be analyzed for optimality. For a case study, a recent commercial design of the quasi-isothermal process is introduced and partially analyzed for its effectiveness. Impact of varying several design factors have been analyzed numerically for further understanding of optimality and for validating the quasi-isothermal nature of the design.

Dynamics of a dissipative, inelastic gravitational billiard

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.

Parametric Study of Spherical Rovers Crossing a Valley

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.