The Experts below are selected from a list of 96 Experts worldwide ranked by ideXlab platform
Christopher D. Hall - One of the best experts on this subject based on the ideXlab platform.
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Minimum-Time Orbital Phasing Maneuvers
2015Co-Authors: Christopher D. Hall, Victor Collazo-perezAbstract:The minimum-time, constant-thrust, orbital Phasing Maneuver is studied numerically. Nondimensionalization reduces the problem to one where thrust magnitude and phase angle are the only parameters. Extremal solutions are obtained for the entire range of practical values of thrust magnitude and phase angle. Plots of trajectories, thrust-angle pro les, and loci of initial costates are used to identify a near-invariance principle that leads to a variety of conclusions about this class of problems. The types of thrust-angle pro les are shown to fall into at least four types, two of which exist within the region of near-invariance. These two thrust-angle pro le types are distinguishedby the time-of- ight tf, and the transition between them takes place for a tf of approximatelyone-half of an orbit. The relationship between tf and the ratio of thrust to phase angle is also shown to be nearly invariant over a wide range of thrust magnitudes
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Minimum-Time Orbital Phasing Maneuvers
2015Co-Authors: Christopher D. Hall, Victor Collazo Perez, Victor Collazo PerezyAbstract:The minimum-time, constant-thrust, orbital Phasing Maneuver is studied numerically. Non-dimensionalization reduces the problem to one where thrust magnitude and phase angle are the only pa-rameters. Extremal solutions are obtained for the entire range of practical values of thrust magnitude and phase angle. Plots of tra-jectories, thrust pro¯les, and loci of initial costates are used to iden-tify a near-invariance principle that leads to a variety of conclusions about this class of problems. The types of thrust pro¯les are shown to fall into at least four types, two of which exist within the region of near-invariance. These two thrust pro¯le types are distinguished by the time-of-°ight, tf, and the transition between them takes place for a tf of approximately one-half of an orbit. The relationship between tf and the ratio of thrust to phase angle is also shown to be nearly invariant over a wide range of thrust magnitudes
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Optimal Electrodynamic Tether Phasing Maneuvers
2007Co-Authors: Matthew S. Bitzer, Christopher D. HallAbstract:We study the minimum-time orbit Phasing Maneuver problem for a constant-current electrodynamic tether (EDT). The EDT is assumed to be a point mass and the electromagnetic forces acting on the tether are always perpendicular to the local magnetic field. After deriving and non-dimensionalizing the equations of motion, the only input parameters become current and the phase angle. Solution examples, including initial Lagrange costates, time of flight, thrust plots, and thrust angle profiles, are given for a wide range of current magnitudes and phase angles. The two-dimensional cases presented use a non-tilted magnetic dipole model, and the solutions are compared to existing literature. We are able to compare similar trajectories for a constant thrust Phasing Maneuver and we find that the time of flight is longer for the constant thrust case with similar initial thrust values and phase angles. Full three-dimensional solutions, which use a titled magnetic dipole model, are also analyzed for orbits with small inclinations.
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F: l̂1, l̂2, l̂3 Magnetic Field Frame
2007Co-Authors: Matthew S. Bitzer, Christopher D. Hall, H Hamiltonian, Tether Direction L VectorAbstract:This paper studies the minimum-time orbit Phasing Maneuver problem for a constant-current electro-dynamic tether (EDT). The EDT is assumed to be a point mass that is always in a plane perpendicular to the local magnetic field. After deriving and non-dimensionalizing the equations of motion, the only input parameters become current and the phase angle. Solution examples, including initial Lagrange costates, time of flight, thrust plots, and thrust angle profiles, are given for a wide range of current magnitudes and phase angles. The two-dimensional cases presented use a non-tilted magnetic dipole model, and the solutions are compared to existing literature. We are able to find similar trajectories to that of a constant thrust Phasing Maneuver, however, the time of flight is shorter. Full three-dimensional solutions, which use a titled magnetic dipole model, are also analyzed for orbits with small inclinations
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Minimum-Time Orbital Phasing Maneuvers
Journal of Guidance Control and Dynamics, 2003Co-Authors: Christopher D. Hall, Victor Collazo-perezAbstract:The minimum-time, constant-thrust, orbital Phasing Maneuver is studied numerically. Nondimensionalization reduces the problem to one where thrust magnitude and phase angle are the only parameters. Extremal solutions are obtained for the entire range of practical values of thrust magnitude and phase angle. Plots of trajectories, thrust-angle proe les, and loci of initial costates are used to identify a near-invariance principle that leads to a variety of conclusions about this class of problems. The types of thrust-angle proe les are shown to fall into at least four types, two of which exist within the region of near-invariance. These two thrust-angle proe le types are distinguished by thetime-of-e ight tf, andthetransition between them takesplacefora tf of approximately one-half of an orbit. The relationship between tf and the ratio of thrust to phase angle is also shown to be nearly invariant over a wide range of thrust magnitudes.
Matthew S. Bitzer - One of the best experts on this subject based on the ideXlab platform.
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Optimal Electrodynamic Tether Phasing and Orbit-Raising Maneuvers
2009Co-Authors: Matthew S. BitzerAbstract:We present optimal solutions for a point-mass electrodynamic tether (EDT) perform-ing Phasing and orbit-raising Maneuvers. An EDT is a conductive tether on the order of 20 km in length and uses a Lorentz force to provide propellantless thrust. We develop the optimal equations of motion using Pontryagin’s Minimum Principle. We find numerical solutions using a global, stochastic optimization method called Adaptive Simulated Annealing. The method uses Markov chains and the system’s cost function to narrow down the search space. Newton’s Method brings the error in the residual to below a specific tolerance. We compare the EDT solutions to simi-lar constant-thrust solutions and investigate the patterns in the solution space. The EDT Phasing Maneuver has invariance properties similar to constant-thrust Phasing Maneuvers. Analyzing the solution space reveals that the EDT is faster at performing Phasing Maneuvers but slower at performing orbit-raising Maneuvers than constant-thrust spacecraft. Also several bifurcation lines occur in the solution spaces for all Maneuvers studied. Acknowledgments I would like to thank Dr. Christopher Hall for all of his advice and all of the oppor-tunities he gave me. I became involved in research and the Aerospace and Ocean Engineering Department because of his encouragement. Those involvements evolve
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Optimal Electrodynamic Tether Phasing Maneuvers
2007Co-Authors: Matthew S. Bitzer, Christopher D. HallAbstract:We study the minimum-time orbit Phasing Maneuver problem for a constant-current electrodynamic tether (EDT). The EDT is assumed to be a point mass and the electromagnetic forces acting on the tether are always perpendicular to the local magnetic field. After deriving and non-dimensionalizing the equations of motion, the only input parameters become current and the phase angle. Solution examples, including initial Lagrange costates, time of flight, thrust plots, and thrust angle profiles, are given for a wide range of current magnitudes and phase angles. The two-dimensional cases presented use a non-tilted magnetic dipole model, and the solutions are compared to existing literature. We are able to compare similar trajectories for a constant thrust Phasing Maneuver and we find that the time of flight is longer for the constant thrust case with similar initial thrust values and phase angles. Full three-dimensional solutions, which use a titled magnetic dipole model, are also analyzed for orbits with small inclinations.
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F: l̂1, l̂2, l̂3 Magnetic Field Frame
2007Co-Authors: Matthew S. Bitzer, Christopher D. Hall, H Hamiltonian, Tether Direction L VectorAbstract:This paper studies the minimum-time orbit Phasing Maneuver problem for a constant-current electro-dynamic tether (EDT). The EDT is assumed to be a point mass that is always in a plane perpendicular to the local magnetic field. After deriving and non-dimensionalizing the equations of motion, the only input parameters become current and the phase angle. Solution examples, including initial Lagrange costates, time of flight, thrust plots, and thrust angle profiles, are given for a wide range of current magnitudes and phase angles. The two-dimensional cases presented use a non-tilted magnetic dipole model, and the solutions are compared to existing literature. We are able to find similar trajectories to that of a constant thrust Phasing Maneuver, however, the time of flight is shorter. Full three-dimensional solutions, which use a titled magnetic dipole model, are also analyzed for orbits with small inclinations
Panagiotis Tsiotras - One of the best experts on this subject based on the ideXlab platform.
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HOHMANN-HOHMANN AND HOHMANN-Phasing COOPERATIVE RENDEZVOUS ManeuverS
2015Co-Authors: Atri Dutta, Panagiotis TsiotrasAbstract:We consider the problem of cooperative rendezvous between two satellites in cir-cular orbits, given a fixed time for the rendezvous to be completed, and assuming a circular rendezvous orbit. We investigate two types of cooperative Maneuvers for which analytical solutions can be obtained. One is the case of two Hohmann trans-fers, while the other, referred to as HPCM, is the case of a Hohmann transfer and a Phasing Maneuver. For the latter case we derive conditions on the Phasing angle that makes a HPCM rendezvous cheaper than a cooperative rendezvous on an orbit that is different than either the original orbits of the two participating satellites. It is shown that minimizing fuel expenditure is equivalent to minimizing a weighted sum of the ΔV s of the two orbital transfers, the weights being determined by the mass and engine characteristics of the satellites. Our results show that, if the time of rendezvous allows for a Hohmann transfer between the orbits of the satellites, the optimal rendezvous is either a non-cooperative Hohmann transfer or a Hohmann-Phasing cooperative Maneuver. In both these cases, the Maneuver costs are deter-mined analytically. A numerical example verifies these observations. Finally, we demonstrate the utility of this study for Peer-to-Peer (P2P) refueling of satellites in two different circular orbits
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Hohmann-Hohmann and Hohmann-Phasing Cooperative Rendezvous Maneuvers
The Journal of the Astronautical Sciences, 2009Co-Authors: Atri Dutta, Panagiotis TsiotrasAbstract:We consider the problem of cooperative rendezvous between two satellites in circular orbits, given a fixed time for the rendezvous to be completed, and assuming a circular rendezvous orbit. We investigate two types of cooperative Maneuvers for which analytical solutions can be obtained. One is the case of two Hohmann transfers, henceforth referred to as HHCM, while the other, henceforth referred to as HPCM, is the case of a Hohmann transfer and a Phasing Maneuver. For the latter case we derive conditions on the Phasing angle that make a HPCM rendezvous cheaper than a cooperative rendezvous on an orbit that is different than either the original orbits of the two participating satellites. It is shown that minimizing the fuel expenditure is equivalent to minimizing a weighted sum of the Δ V s of the two orbital transfers, the weights being determined by the mass and engine characteristics of the satellites. Our results show that, if the time of rendezvous allows for a Hohmann transfer between the orbits of the satellites, the optimal rendezvous is either a noncooperative Hohmann transfer or a Hohmann-Phasing cooperative Maneuver. In both of these cases, the Maneuver costs are determined analytically. A numerical example verifies these observations. Finally, we demonstrate the utility of this study for Peer-to-Peer (P2P) refueling of satellites residing in two different circular orbits.
Atri Dutta - One of the best experts on this subject based on the ideXlab platform.
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HOHMANN-HOHMANN AND HOHMANN-Phasing COOPERATIVE RENDEZVOUS ManeuverS
2015Co-Authors: Atri Dutta, Panagiotis TsiotrasAbstract:We consider the problem of cooperative rendezvous between two satellites in cir-cular orbits, given a fixed time for the rendezvous to be completed, and assuming a circular rendezvous orbit. We investigate two types of cooperative Maneuvers for which analytical solutions can be obtained. One is the case of two Hohmann trans-fers, while the other, referred to as HPCM, is the case of a Hohmann transfer and a Phasing Maneuver. For the latter case we derive conditions on the Phasing angle that makes a HPCM rendezvous cheaper than a cooperative rendezvous on an orbit that is different than either the original orbits of the two participating satellites. It is shown that minimizing fuel expenditure is equivalent to minimizing a weighted sum of the ΔV s of the two orbital transfers, the weights being determined by the mass and engine characteristics of the satellites. Our results show that, if the time of rendezvous allows for a Hohmann transfer between the orbits of the satellites, the optimal rendezvous is either a non-cooperative Hohmann transfer or a Hohmann-Phasing cooperative Maneuver. In both these cases, the Maneuver costs are deter-mined analytically. A numerical example verifies these observations. Finally, we demonstrate the utility of this study for Peer-to-Peer (P2P) refueling of satellites in two different circular orbits
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Hohmann-Hohmann and Hohmann-Phasing Cooperative Rendezvous Maneuvers
The Journal of the Astronautical Sciences, 2009Co-Authors: Atri Dutta, Panagiotis TsiotrasAbstract:We consider the problem of cooperative rendezvous between two satellites in circular orbits, given a fixed time for the rendezvous to be completed, and assuming a circular rendezvous orbit. We investigate two types of cooperative Maneuvers for which analytical solutions can be obtained. One is the case of two Hohmann transfers, henceforth referred to as HHCM, while the other, henceforth referred to as HPCM, is the case of a Hohmann transfer and a Phasing Maneuver. For the latter case we derive conditions on the Phasing angle that make a HPCM rendezvous cheaper than a cooperative rendezvous on an orbit that is different than either the original orbits of the two participating satellites. It is shown that minimizing the fuel expenditure is equivalent to minimizing a weighted sum of the Δ V s of the two orbital transfers, the weights being determined by the mass and engine characteristics of the satellites. Our results show that, if the time of rendezvous allows for a Hohmann transfer between the orbits of the satellites, the optimal rendezvous is either a noncooperative Hohmann transfer or a Hohmann-Phasing cooperative Maneuver. In both of these cases, the Maneuver costs are determined analytically. A numerical example verifies these observations. Finally, we demonstrate the utility of this study for Peer-to-Peer (P2P) refueling of satellites residing in two different circular orbits.
Victor Collazo-perez - One of the best experts on this subject based on the ideXlab platform.
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Minimum-Time Orbital Phasing Maneuvers
2015Co-Authors: Christopher D. Hall, Victor Collazo-perezAbstract:The minimum-time, constant-thrust, orbital Phasing Maneuver is studied numerically. Nondimensionalization reduces the problem to one where thrust magnitude and phase angle are the only parameters. Extremal solutions are obtained for the entire range of practical values of thrust magnitude and phase angle. Plots of trajectories, thrust-angle pro les, and loci of initial costates are used to identify a near-invariance principle that leads to a variety of conclusions about this class of problems. The types of thrust-angle pro les are shown to fall into at least four types, two of which exist within the region of near-invariance. These two thrust-angle pro le types are distinguishedby the time-of- ight tf, and the transition between them takes place for a tf of approximatelyone-half of an orbit. The relationship between tf and the ratio of thrust to phase angle is also shown to be nearly invariant over a wide range of thrust magnitudes
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Minimum-Time Orbital Phasing Maneuvers
Journal of Guidance Control and Dynamics, 2003Co-Authors: Christopher D. Hall, Victor Collazo-perezAbstract:The minimum-time, constant-thrust, orbital Phasing Maneuver is studied numerically. Nondimensionalization reduces the problem to one where thrust magnitude and phase angle are the only parameters. Extremal solutions are obtained for the entire range of practical values of thrust magnitude and phase angle. Plots of trajectories, thrust-angle proe les, and loci of initial costates are used to identify a near-invariance principle that leads to a variety of conclusions about this class of problems. The types of thrust-angle proe les are shown to fall into at least four types, two of which exist within the region of near-invariance. These two thrust-angle proe le types are distinguished by thetime-of-e ight tf, andthetransition between them takesplacefora tf of approximately one-half of an orbit. The relationship between tf and the ratio of thrust to phase angle is also shown to be nearly invariant over a wide range of thrust magnitudes.