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تحلیل آشوب و طراحی مسیر در فضای چهارجسم
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تحلیل آشوب و طراحی مسیر در فضای چهارجسم

سینجلی، محمد Sayanjali, Mohammad

Chaos Analysis and Trajectory Design in Four Body Problem

Sayanjali, Mohammad | 2015

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 47965 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Pourtakdoust, Hossein
  7. Abstract:
  8. The subject of low thrust transfer trajectory design to the Sun-Earth L2 Lagrange point, considering the Moon’s gravitational attraction as the fourth body effect has been investigated. In addition, three body resonance orbits chaotic dynamics are also studied. The problem of transfer trajectory design to Earth-Moon halo orbit is investigated using two approaches for the thrusting phase of flight.In the first approach, a complete Bicircular four body model is utilized to initially insert an Earth bound spacecraft via active low thrust propulsion on a stable manifold (SM) of the Earth-Moon three body system. Subsequently, the spacecraft coasts to its desired Halo orbit with minimum Trajectory Correction Maneuvers (TCM). This problem is scrutinized for various parameters that include the final Halo injection point (HIP) and the Moon’s angle at HIP, as well as the effect of thrust cut off location on the accuracy of SM insertion and HIP. The results indicate that there are some regions or HIPs, transfer to which are highly sensitive with respect to SM insertion that cause a significant deviation either from the desired passive coasting trajectory to the final HIP or require significant TCM to stay on the desired Halo orbit.In the second approach, a covariance trajectory shaping method aimed at minimization of SM insertion error is utilized while the design is in the Sun-Earth circular restricted three body (CRTB) environment under the Moon’s gravitational perturbation. In this scheme the state vectors are augmented with the spacecraft position and velocity covariance propagation equations that is collectively optimized in the optimal control formulation. Though this scheme has reduced SM insertion error, it is not significantly effective in comparison with the first full four body approach.The analytical part of the dissertation deals with application of various chaos detection tools to investigate chaos in special orbits in a simulated four body environment. In this regard the effects of the Sun’s gravitation on the Earth-Moon CRTB resonance orbits are investigated via Melnikov method. The result indicate that for certain three body resonance conditions the orbits , inclusion of the fourth body gravitational perturbation could cause chaotic behavior. This phenomenon is further verified via other numerical means of chaos detection such as the fast Lyapunov indicators and the time frequency analysis
  9. Keywords:
  10. Low-Thrust Propulsion ; Chaos Theory ; Transfer Trajectory Design ; Four Body Problem ; Resonance Orbit

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