Spelling suggestions: "subject:"circular restricted three body 3dproblem"" "subject:"circular restricted three body 23problem""
1 
Trade Study of Decomissioning Strategies for the International Space StationHerbort, Eric 06 September 2012 (has links)
This thesis evaluates decommissioning strategies for the International Space Station ISS. A permanent solution is attempted by employing energy efficient invariant manifolds that arise in the circular restricted three body problem CRTBP to transport the ISS from its low Earth orbit LEO to a lunar orbit. Although the invariant manifolds provide efficient transport, getting the the ISS onto the manifolds proves quite expensive, and the trajectories take too long to complete. Therefore a more practical, although temporary, solution consisting of an optimal reboost maneuver with the European Space Agency's automated transfer vehicle ATV is proposed. The optimal reboost trajectory is found using control parameterization and the sequential quadratic programming SQP algorithm. The model used for optimization takes into account the affects of atmospheric drag and gravity perturbations. The optimal reboost maneuver produces a satellite lifetime of approximately ninetyfive years using a two ATV strategy.

2 
Hybrid StationKeeping Controller Design Leveraging Floquet Mode and Reinforcement Learning ApproachesAndrew Blaine Molnar (9746054) 15 December 2020 (has links)
The general stationkeeping problem is a focal topic when considering any spacecraft mission application. Recent missions are increasingly requiring complex trajectories to satisfy mission requirements, necessitating the need for accurate stationkeeping controllers. An ideal controller reliably corrects for spacecraft state error,
minimizes the required propellant, and is computationally efficient. To that end,
this investigation assesses the effectiveness of several controller formulations in the
circular restricted threebody model. Particularly, a spacecraft is positioned in a L<sub>1</sub> southern halo orbit within the SunEarth Moon Barycenter system. To prevent the
spacecraft from departing the vicinity of this reference halo orbit, the Floquet mode
stationkeeping approach is introduced and evaluated. While this control strategy
generally succeeds in the stationkeeping objective, a breakdown in performance is
observed proportional to increases in state error. Therefore, a new hybrid controller
is developed which leverages Floquet mode and reinforcement learning. The hybrid
controller is observed to efficiently determine corrective maneuvers that consistently
recover the reference orbit for all evaluated scenarios. A comparative analysis of the
performance metrics of both control strategies is conducted, highlighting differences
in the rates of success and the expected propellant costs. The performance comparison demonstrates a relative improvement in the ability of the hybrid controller to
meet the mission objectives, and suggests the applicability of reinforcement learning
to the stationkeeping problem.

3 
Characterization of Lunar Access Relative to Cislunar OrbitsRolfe J Power IV (8081426) 04 December 2019
With the growth of human interest in the Lunar region, methods of enabling Lunar access including surface and Low Lunar Orbit (LLO) from periodic orbit in the Lunar region is becoming more important. The current investigation explores the Lunar access capabilities of these periodic orbits. Impact trajectories originating from the 9:2 Lunar Synodic Resonant (LSR) Near Rectilinear Halo Orbit (NRHO) are determined through explicit propagation and mapping of initial conditions formed by applying small maneuvers at locations across the orbit. These trajectories yielding desirable Lunar impact final conditions are then used to converge impacting transfers from the NRHO to Shackleton crater near the Lunar south pole. The stability of periodic orbits in the Lunar region is analyzed through application of a stability index and time constant. The Lunar access capabilities of the Lunar region periodic orbits found to be sufficiently unstable are then analyzed through impact and periapse maps. Using the impact data, candidate periodic orbits are incorporated in the the NRHO to Shackleton crater mission design to control mission geometry. Finally, the periapse map data is used to determine periodic orbits with desirable apse conditions that are then used to design NRHO to LLO transfer trajectories.

4 
Finding Order in Chaos: Resonant Orbits and Poincaré SectionsMaaninee Gupta (8770355) 01 May 2020 (has links)
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<p>Resonant orbits in a multibody environment have been investigated in the past to
aid the understanding of perceived chaotic behavior in the solar system. The invariant manifolds associated with resonant orbits have also been recently incorporated
into the design of trajectories requiring reduced maneuver costs. Poincaré sections
are now also extensively utilized in the search for novel, maneuverfree trajectories
in various systems. This investigation employs dynamical systems techniques in the
computation and characterization of resonant orbits in the higherfidelity Circular
Restricted ThreeBody model. Differential corrections and numerical methods are
widely leveraged in this analysis in the determination of orbits corresponding to different resonance ratios. The versatility of resonant orbits in the design of low cost
trajectories to support exploration for several planetmoon systems is demonstrated.
The efficacy of the resonant orbits is illustrated via transfer trajectory design in the
EarthMoon, SaturnTitan, and the MarsDeimos systems. Lastly, Poincaré sections
associated with different resonance ratios are incorporated into the search for natural,
maneuverfree trajectories in the SaturnTitan system. To that end, homoclinic and
heteroclinic trajectories are constructed. Additionally, chains of periodic orbits that
mimic the geometries for two different resonant ratios are examined, i.e., periodic orbits that cycle between different resonances are determined. The tools and techniques
demonstrated in this investigation are useful for the design of trajectories in several
different systems within the CR3BP.
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5 
Trajectory Design and Targeting For Applications to the Exploration Program in Cislunar SpaceEmily MZ Spreen (10665798) 07 May 2021 (has links)
<p>A dynamical understanding of orbits in the EarthMoon
neighborhood that can sustain longterm activities and trajectories that link
locations of interest forms a critical foundation for the creation of
infrastructure to support a lasting presence in this region of space. In response, this investigation aims to
identify and exploit fundamental dynamical motion in the vicinity of a
candidate ‘hub’ orbit, the L2 southern 9:2 lunar synodic resonant near
rectilinear halo orbit (NRHO), while incorporating realistic mission
constraints. The strategies developed in
this investigation are, however, not restricted to this particular orbit but
are, in fact, applicable to a wide variety of stable and nearlystable cislunar
orbits. Since stable and nearlystable
orbits that may lack useful manifold structures are of interest for longterm
activities in cislunar space due to low orbit maintenance costs, strategies to
alternatively initiate transfer design into and out of these orbits are
necessary. Additionally, it is crucial
to understand the complex behaviors in the neighborhood of any candidate hub
orbit. In this investigation, a
bifurcation analysis is used to identify periodic orbit families in close
proximity to the hub orbit that may possess members with favorable stability
properties, i.e., unstable orbits.
Stability properties are quantified using a metric defined as the stability
index. Broucke stability diagrams, a
tool in which the eigenvalues of the monodromy matrix are recast into two
simple parameters, are used to identify bifurcations along orbit families. Continuation algorithms, in combination with
a differential corrections scheme, are used to compute new families of periodic
orbits originating at bifurcations.
These families possess unstable members with associated invariant
manifolds that are indeed useful for trajectory design. Members of the families nearby the L2 NRHOs
are demonstrated to persist in a higherfidelity ephemeris model. </p><p><br></p>
<p>Transfers based on the identified nearby dynamical
structures and their associated manifolds are designed. To formulate initial guesses for transfer
trajectories, a Poincaré mapping technique is used. Various sample trajectory designs are
produced in this investigation to demonstrate the wide applicability of the
design methodology. Initially, designs
are based in the circular restricted threebody problem, however, geometries
are demonstrated to persist in a higherfidelity ephemeris model, as well. A strategy to avoid Earth and Moon eclipse
conditions along manyrevolution quasiperiodic ephemeris orbits and transfer
trajectories is proposed in response to upcoming mission needs. Lunar synodic resonance, in combination with
careful epoch selection, produces a simple eclipseavoidance technique. Additionally, an integraltype eclipse
avoidance path constraint is derived and incorporated into a differential
corrections scheme as well. Finally,
transfer trajectories in the circular restricted threebody problem and
higherfidelity ephemeris model are optimized and the geometry is shown to
persist.</p>

6 
Cislunar Mission Design: Transfers Linking Near Rectilinear Halo Orbits and the Butterfly FamilyMatthew John Bolliger (7165625) 16 October 2019 (has links)
An integral part of NASA's vision for the coming years is a sustained infrastructure in cislunar space. The current baseline trajectory for this facility is a Near Rectilinear Halo Orbit (NRHO), a periodic orbit in the Circular Restricted ThreeBody Problem. One of the goals of the facility is to serve as a proving ground for human spaceflight operations in deep space. Thus, this investigation focuses on transfers between the baseline NRHO and a family of periodic orbits that originate from a perioddoubling bifurcation along the halo family. This new family of orbits has been termed the ``butterfly" family. This investigation also provides an overview of the evolution for a large subset of the butterfly family. Transfers to multiple subsets of the family are found by leveraging different design strategies and techniques from dynamical systems theory. The different design strategies are discussed in detail, and the transfers to each of these regions are compared in terms of propellant costs and times of flight.

7 
Construction of Ballistic Lunar Transfers in the EarthMoonSun SystemStephen Scheuerle Jr. (10676634) 07 May 2021 (has links)
<p>An increasing interest in lunar
exploration calls for lowcost techniques of reaching the Moon. Ballistic lunar
transfers are long duration trajectories that leverage solar perturbations to
reduce the multibody energy of a spacecraft upon arrival into cislunar space.
An investigation is conducted to explore methods of constructing ballistic
lunar transfers. The techniques employ dynamical systems theory to leverage the
underlying dynamical flow of the multibody regime. Ballistic lunar transfers
are governed by the gravitational influence of the EarthMoonSun system; thus,
multibody gravity models are employed, i.e., the circular restricted
threebody problem (CR3BP) and the bicircular restricted fourbody problem (BCR4BP).
The SunEarth CR3BP provides insight into the Sun’s effect on transfers near the
Earth. The BCR4BP offers a coherent model for constructing endtoend ballistic
lunar transfers. Multiple techniques are employed to uncover ballistic
transfers to conic and multibody orbits in cislunar space. Initial conditions
to deliver the spacecraft into various orbits emerge from Periapse Poincaré
maps. From a chosen geometry, families of transfers from the Earth to conic
orbits about the Moon are developed. Instantaneous equilibrium solutions in the
BCR4BP provide an approximate for the theoretical minimum lunar orbit insertion
costs, and are leveraged to create lowcost solutions. Trajectories to the <i>L</i>2 2:1 synodic resonant Lyapunov orbit, <i>L</i>2 2:1 synodic resonant Halo orbit, and the 3:1 synodic resonant
Distant Retrograde Orbit (DRO) are investigated.</p>

8 
MultiBody Trajectory Design in the EarthMoon Region Utilizing Poincare MapsPaige Alana Whittington (12455871) 25 April 2022 (has links)
<p>The 9:2 lunar synodic resonant near rectilinear halo orbit (NRHO) is the chosen orbit for the Gateway, a future lunar space station constructed by the National Aeronautics and Space Administration (NASA) as well as several commercial and international partners. Designing trajectories in this sensitive lunar region combined with the absence of a singular systematic methodology to approach mission design poses challenges as researchers attempt to design transfers to and from this nearly stable orbit. This investigation builds on previous research in Poincar\'e mapping strategies to design transfers from the 9:2 NRHO using higherdimensional maps and maps with nonstate variables. First, Poincar\'e maps are applied to planar transfers to demonstrate the utility of hyperplanes and establish that maps with only two or three dimensions are required in the planar problem. However, with the addition of two state variables, the spatial problem presents challenges in visualizing the full state. Higherdimensional maps utilizing glyphs and color are employed for spatial transfer design involving the 9:2 NRHO. The visualization of all required dimensions on one plot accurately reveals low cost transfers into both a 3:2 planar resonant orbit and an L2 vertical orbit. Next, the application of higherdimensional maps is extended beyond state variables. Visualizing timeofflight on a map axis enables the selection of faster transfers. Additionally, glyphs and color depicting angular momentum rather than velocity lead to transfers with nearly tangential maneuvers. Theoretical minimum maneuvers occur at tangential intersections, so these transfers are low cost. Finally, a map displaying several initial and final orbit options, discerned through the inclusion of Jacobi constant on an axis, eliminates the need to recompute a map for each initial and final orbit pair. Thus, computation time is greatly reduced in addition to visualizing more of the design space in one plot. The higherdimensional mapping strategies investigated are relevant for transfer design or other applications requiring the visualization of several dimensions simultaneously. Overall, this investigation outlines Poincar\'e mapping strategies for transfer scenarios of different design space dimensions and represents initial research into nonstate variable mapping methods.</p>

9 
There and Back Again: Generating Repeating Transfers Using Resonant StructuresNoah Isaac Sadaka (15354313) 25 April 2023 (has links)
<p>Many future satellite applications in cislunar space require repeating, periodic transfers that shift away from some operational orbit and eventually return. Resonant orbits are investigated in the EarthMoon Circular Restricted Three Body Problem (CR3BP) as a mechanism to enable these transfers. Numerous resonant orbit families possess a ratio of orbital period to lunar period that is sufficiently close to an integer ratio and can be exploited to uncover periodcommensurate transfers due to their predictable periods. Resonant orbits also collectively explore large swaths of space, making it possible to select specific orbits that reach a region of interest. A framework for defining periodcommensurate transfers is introduced that leverages the homoclinic connections associated with an unstable operating orbit to permit ballistic transfers that shuttle the spacecraft to a certain region. Resonant orbits are incorporated by locating homoclinic connections that possess resonant structures, and the applicability of these transfers is extended by optionally linking them to resonant orbits. In doing so, transfers are available for inorbit refueling/maintenance as well as surveillance/communications applications that depart and return to the same phase in the operating orbit.</p>

10 
Dynamical Flow Characteristics in Response to a Maneuver in the L1 or L2 EarthMoon RegionColton D Mitchell (15347518) 25 April 2023 (has links)
<p>National security concerns regarding cislunar space have become more prominent due to</p>
<p>the anticipated increase in cislunar activity. Predictability is one of these concerns. Cislunar</p>
<p>motion is difficult to predict because it is chaotic. The chaotic nature of cislunar motion is</p>
<p>pronounced near the L1 and L2 Lagrange points. For this reason, among others, it is likely</p>
<p>that a red actor (an antagonist) would have its cislunar spacecraft perform a maneuver in</p>
<p>one of the aforementioned vicinities to reach some cislunar point of interest. This realization</p>
<p>unveils the need to ascertain some degree of predictability in the motion resulting from a</p>
<p>maneuver performed in the L1 or L2 region. To investigate said motion, impulsive maneuvers</p>
<p>are employed on the L1 and L2 Lagrange points and on L1 and L2 Lyapunov orbits in the</p>
<p>model that is the circular restricted threebody problem. The behavior of the resultant</p>
<p>trajectories is analyzed to understand how the magnitude and direction of a maneuver in</p>
<p>said regions affect the behavior of the resultant trajectory. It is found that the direction</p>
<p>of such maneuvers is particularly influential with respect to said behavior. Regarding both</p>
<p>the L1 and L2 regions, certain maneuver directions yield certain behaviors in the resultant</p>
<p>trajectory over a wide range of maneuver magnitudes. This understanding is informative to</p>
<p>cislunar mission design.</p>

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