Gerard Gomez | Universitat de Barcelona (original) (raw)

Papers by Gerard Gomez

Research paper thumbnail of Pseudo-heteroclinic connections between bicircular restricted four-body problems

Monthly Notices of the Royal Astronomical Society, Jul 11, 2016

Research paper thumbnail of Expansions Required for the Equations of Motion: Collinear Points Case

Research paper thumbnail of Advanced methods for triangylar points

Global stability zones around the triangular libration points the normal form around L5 in the th... more Global stability zones around the triangular libration points the normal form around L5 in the three-dimensional RTBP normal form of the bicircular model and related topics the quasi-periodic model nominal paths and stability properties transfer to orbits in a vicinity of the Lagrangian points. Appendices: global stability zones around the triangular libration points in the elliptic RTBP Fourier analysis geometrical bounds for the dynamics - codimension 1 manifolds.

Research paper thumbnail of Libration Transfer Design Using Patched Elliptic Three-Body Models and Graphics Processing Units

Journal of Guidance, Control, and Dynamics, 2017

Design of the transfer from lunar orbits to the Sun-Earth libration point region by direct search... more Design of the transfer from lunar orbits to the Sun-Earth libration point region by direct searching in the high-delity ephemeris model is an accurate but time-consuming practice. We present a computationally ecient methodology that takes advantage of the Patched Elliptic Restricted Three-Body Problem (ERTBP) model, the power of Graphics Processing Unit (GPU) parallel computing, and the programing platform of the Matlab. Taking the Chang'E-2 extension mission as an instance, the proposed implementation obtains almost identical results with that in the ephemeris model and shows signicant speedup. Moreover, the methodology can be carried out on inexpensive hardware platforms. Numerical results demonstrate that signicant speedups can be achieved using the GPU parallel computing in Matlab with a little learning cost.

Research paper thumbnail of Dynamic Mechanisms for Spacecraft Disposal from Sun–Earth Libration Points

Journal of Guidance, Control, and Dynamics, 2015

This work investigates end-of-life trajectories for spacecraft in orbit about the sun–Earth L1

Research paper thumbnail of Transport Dynamics: From the Bicircular to the Real Solar System Problem

Trends in Mathematics, 2015

Research paper thumbnail of Study on the station keeping maintenance for the tpf mission

In 1995, Mayor and Queloz [a] detected for the first time a planet orbiting a nearby star (15.4 p... more In 1995, Mayor and Queloz [a] detected for the first time a planet orbiting a nearby star (15.4 parsecs). Since then, the interest in the detection of extra-solar planets, in order to learn about the origin, evolution, and composition of planetary systems, has grown tremendously and ...

Research paper thumbnail of Dynamics in the Center Manifold around Equilibrium Points in Periodically-Perturbed Three-body Problems

A new application of the parameterization method is presented to compute invariant manifolds abou... more A new application of the parameterization method is presented to compute invariant manifolds about the equilibrium points of Periodically Perturbed Three-Body Problems (PPTBP). These techniques are applied to obtain high-order semi-numerical approximations of the center manifolds about the points L 1,2 of the Sun-perturbed Earth-Moon Quasi-Bicicular Problem (QBCP), which is a particular case of PPTBP. The quality of these approximations is compared with results obtained using equivalents of previous normal form procedures. Then, the parameterization is used to initialize the computation of Poincaré maps, which allow to get a qualitative description of the periodically-perturbed dynamics near the equilibrium points.

Research paper thumbnail of Low-energy trajectory design and autonomous navigation to flyby near-Earth asteroids using CubeSats

In response to the current interest in CubeSats and potential applications for planetary explorat... more In response to the current interest in CubeSats and potential applications for planetary exploration, this work studies the feasibility of using autonomous CubeSats to flyby near-Earth asteroids. Considering the limited performance of current propulsion systems for CubeSats, low-energy (impulsive and low-thrust) trajectories are designed to encounter near-Earth asteroids in the medium-fidelity Circular Restricted Three-Body Problem, and their existence in a high-fidelity ephemeris model is also verified. The use of large ground antennas for deep-space communications might represent a major portion of CubeSat mission budgets, and thus the feasibility of performing optical navigation to autonomously estimate and correct the trajectory of the CubeSat is also evaluated through Monte Carlo simulations. Preliminary results show that approximately 4 asteroids per year could be reached by a 3U CubeSat if deployed around the first or second Sun-Earth Lagrange points. According to the limited...

Research paper thumbnail of Astrodynamics Network AstroNet-II

AstroNet-II has been the European Research Training Network that has trained through research eig... more AstroNet-II has been the European Research Training Network that has trained through research eighteen young scientist and engineers on a number of problems in astrodynamics, all of them of current interest to space agencies and industry. Fourteen partners composed the network, eight of them university departments and research institutes, and the remaining six aerospace companies and space agencies. During its execution (2012-2015) AstroNet-II has been coordinated by the Institut d'Estudis Espacials de Catalunya (IEEC) in Barcelona (www.ieec.cat). The network has organized four Training Schools, open to young researchers not enrolled in AstroNet-II, in which the following short courses were given by some of the best specialist in the field: An introduction in which the following short courses were given by some of the best specialist in the field: An introduction to Differential Algebra, An introduction to MATLAB®/SIMULINK®

Research paper thumbnail of Global analysis of direct transfers from Lunar orbits to Sun-Earth libration point regimes

Celestial Mechanics and Dynamical Astronomy, 2021

In this paper we look forward to obtain a global picture of simple transfer opportunities from Lu... more In this paper we look forward to obtain a global picture of simple transfer opportunities from Lunar to Sun-Earth libration orbits, useful for a preliminary design of these mission scenarios. Considering the trajectory of the Chinese Change’2 spacecraft as a reference case, the main transfer families are characterized and classified. In a second step, the results are analyzed and extended to departures from more general families of orbits about the Moon. Finally, we also include a preliminary sensitivity analysis of the first transfer correction maneuver (TCM1) to cancel injection errors. The methodology is of general applicability to the transfer analysis involving libration point final orbits in other general multi-body restricted systems.

Research paper thumbnail of Systematic study of the dynamics about and between the Libration Points of the Sun-Earth-Moon System

A new approach is proposed for systematic detection and refinement of natural connections EML12 o... more A new approach is proposed for systematic detection and refinement of natural connections EML12 of the Earth-Moon system and SEML12 of Sun-Earth-Moon. It is structured around the Quasi-Bircircular Problem, a restricted coherent and periodic four-body dynamical model of the Sun-Earth-Moon system. The dynamics about the Libration points are described by high-order periodic semi-analytical expansions obtained via the parametrization method.

Research paper thumbnail of Rotation–translation coupling analysis on perturbed spacecraft relative translational motion

Nonlinear Dynamics, 2020

This paper explores an accurate and complete spacecraft six-degrees-of-freedom coupled relative m... more This paper explores an accurate and complete spacecraft six-degrees-of-freedom coupled relative motion model using the dual quaternion representation. Based on this technique, we build a scheme capable of describing both kinematic and dynamic coupling effects on the spacecraft relative translational motion through a further combination with the chaser's precise absolute translational and rotational dynamics. This new model generalizes the existing nonlinear spacecraft relative translational model to include both the kinematic coupling effect due to the displacements of selected feature points relative to the spacecraft centers of mass and the dynamic coupling effect induced by the gravity gradient torque and the orbital perturbations. Several numerical simulations are implemented to validate the

Research paper thumbnail of Analysis of Jet Transport-Based Geostationary Trajectory Uncertainty Propagation

Journal of Guidance, Control, and Dynamics, 2020

This paper investigates an accurate and efficient nonlinear method for propagating geostationary ... more This paper investigates an accurate and efficient nonlinear method for propagating geostationary trajectory uncertainties under four dominant perturbations: solar radiation pressure, Earth's non-spherical gravity potential, and luni-solar gravitational attractions. A Jet Transport-based scheme (also known as Differential Algebra) is considered and implemented in several coordinate representations, and in two forms: Taylor and Chebyshev expansions. Taking into account the size of the uncertainty neighborhood, as well as the order and time

Research paper thumbnail of High-fidelity trajectory design to flyby near-Earth asteroids using CubeSats

Acta Astronautica, 2019

Fast development of CubeSat technology now enables the first interplanetary missions. The potenti... more Fast development of CubeSat technology now enables the first interplanetary missions. The potential application of CubeSats to flyby near-Earth asteroids is explored in this paper in consideration of CubeSats' limited propulsive capabilities and systems constraints. Low-energy asteroid flyby trajectories are designed assuming a CubeSat is initially parked around to the Sun-Earth Lagrange points. High-impulse and low-thrust trajectories with realistic thrusting models are computed first in the Circular Restricted Three-Body Problem (CR3BP), and then in a high-fidelity ephemeris model. Analysis in the ephemeris model is used to confirm that trajectories computed in the CR3BP model also exist in a more realistic dynamical model, and to verify the validity of the results obtained in CR3BP analysis. A catalogue of asteroid flyby opportunities between years 2019 and 2030 is provided, with 80 m/s of available ΔV and departure from halo orbits around the first and second Sun-Earth Lagrange points (of similar size to those typically used by scientific missions). Results show that the CR3BP model can serve as an effective tool to identify reachable asteroids and can provide an initial estimation of the ΔV cost in the ephemeris model (with ±15 m/s accuracy). An impulsive maneuver model can also provide an accurate estimation of the ΔV requirement for a CubeSat equipped with a high-impulse thruster (with 4 m/s accuracy), even if its thrust magnitude is small and requires duty cycling; low-thrust ΔV requirements, however, may differ significantly from the impulsive results (±15 m/s).

Research paper thumbnail of A new subdivision algorithm for the flow propagation using polynomial algebras

Communications in Nonlinear Science and Numerical Simulation, 2018

The Jet Transport method has emerged as a powerful tool for the numerical integration of ordinary... more The Jet Transport method has emerged as a powerful tool for the numerical integration of ordinary differential equations; it uses polynomial expansions to approximate the flow map associated to the differential equation in the neighborhood of a reference solution. One of the main drawbacks of the method is that the region of accuracy becomes smaller along the integration. In this paper we introduce a procedure to determine a ball covering the set of given initial conditions that keeps the accuracy of the integration within a selected threshold. The paper gives detailed explanations of the algorithm illustrated with some examples of applicability, as well as a comparison with a previous existing method for the same purpose.

Research paper thumbnail of Relative Dynamics of Charged Spacecraft in a Magnetic Field applied to Formation Flight

Communications in Nonlinear Science and Numerical Simulation, 2019

We consider several charged spacecraft configurations around a leader spacecraft provided with an... more We consider several charged spacecraft configurations around a leader spacecraft provided with an artificial magnetic field. In all configurations the nominal orbits are chosen to be about the relative equilibrium points of the reference model. Using a linear quadratic regulator controller, we find that controllability is possible in most of the cases, and it is strongly related to the stability of the equilibrium point which, in turn, depends on the orbit of the leader and the rotation rate of its magnetic dipole. The dynamical model considered shows a great potential for future formation flying applications since both, the establishment and maintenance of the configurations, can be managed by merely adjusting the charge on the follower spacecraft. No additional control variables are needed.

Research paper thumbnail of Analysis of the relative dynamics of a charged spacecraft moving under the influence of a magnetic field

Communications in Nonlinear Science and Numerical Simulation, 2018

We analyse a dynamical scenario where a constantly charged spacecraft (follower) moves in the vic... more We analyse a dynamical scenario where a constantly charged spacecraft (follower) moves in the vicinity of another one (leader) that follows a circular Keplerian orbit around the Earth and generates a rotating magnetic dipole. The mass of the follower is assumed to be negligible when compared with the one of the leader and they are supposed to be in a high-Earth orbit, so the Lorentz force on the follower due to the geomagnetic field is ignored. With these as

Research paper thumbnail of Jet transport-based nonlinear state and parameter estimation for geostationary spacecraft

Acta Astronautica, 2019

Based on the jet transport technique, this paper proposes a novel nonlinear Kalman filter for sim... more Based on the jet transport technique, this paper proposes a novel nonlinear Kalman filter for simultaneously estimating the spacecraft state vector and uncertain parameters, either physically related with the spacecraft or with the measurement procedure. Two different coordinate representations, including Cartesian and hybrid geostationary orbital elements, are exploited in the new nonlinear estimators. The performance and sensitivity analyses of the proposed jet transport-based nonlinear estimators are assessed by numerical simulations and compared with the classical extended Kalman filter.

Research paper thumbnail of Invariant manifolds of a non-autonomous quasi-bicircular problem computed via the parameterization method

Nonlinearity, 2017

A new application of the parameterization method is presented to compute invariant manifolds abou... more A new application of the parameterization method is presented to compute invariant manifolds about the libration points of the Sun-Earth-Moon system. The Sun-Earth-Moon environment is modeled by the so-called Quasi-Bicircular Model (qbcp), which is a coherent restricted four-body model that describes the motion of a spacecraft under the simultaneous gravitational influence of the Earth, the Moon, and the Sun. This model can alternatively be seen as a Sun-perturbed Earth-Moon system or a Moon-perturbed Sun-Earth system, both being periodically-perturbed restricted three-body problems (pptbp). The recent parameterization method is applied to obtain high-order, time-dependent, semi-analytical approximations of the center manifolds about the points L 1,2 of these two pptbps. These approximations are then used to initialize the computation of Poincaré maps, which allow to get a qualitative description of the periodically-perturbed dynamics near the equilibrium points. It is shown that, with this new approach, the semi-analytical description of the center manifolds in a coherent four-body environment is valid in a neighborhood significant enough to be used in practice. In particular, the well-known Halo orbit bifurcation is recovered in all cases.

Research paper thumbnail of Pseudo-heteroclinic connections between bicircular restricted four-body problems

Monthly Notices of the Royal Astronomical Society, Jul 11, 2016

Research paper thumbnail of Expansions Required for the Equations of Motion: Collinear Points Case

Research paper thumbnail of Advanced methods for triangylar points

Global stability zones around the triangular libration points the normal form around L5 in the th... more Global stability zones around the triangular libration points the normal form around L5 in the three-dimensional RTBP normal form of the bicircular model and related topics the quasi-periodic model nominal paths and stability properties transfer to orbits in a vicinity of the Lagrangian points. Appendices: global stability zones around the triangular libration points in the elliptic RTBP Fourier analysis geometrical bounds for the dynamics - codimension 1 manifolds.

Research paper thumbnail of Libration Transfer Design Using Patched Elliptic Three-Body Models and Graphics Processing Units

Journal of Guidance, Control, and Dynamics, 2017

Design of the transfer from lunar orbits to the Sun-Earth libration point region by direct search... more Design of the transfer from lunar orbits to the Sun-Earth libration point region by direct searching in the high-delity ephemeris model is an accurate but time-consuming practice. We present a computationally ecient methodology that takes advantage of the Patched Elliptic Restricted Three-Body Problem (ERTBP) model, the power of Graphics Processing Unit (GPU) parallel computing, and the programing platform of the Matlab. Taking the Chang'E-2 extension mission as an instance, the proposed implementation obtains almost identical results with that in the ephemeris model and shows signicant speedup. Moreover, the methodology can be carried out on inexpensive hardware platforms. Numerical results demonstrate that signicant speedups can be achieved using the GPU parallel computing in Matlab with a little learning cost.

Research paper thumbnail of Dynamic Mechanisms for Spacecraft Disposal from Sun–Earth Libration Points

Journal of Guidance, Control, and Dynamics, 2015

This work investigates end-of-life trajectories for spacecraft in orbit about the sun–Earth L1

Research paper thumbnail of Transport Dynamics: From the Bicircular to the Real Solar System Problem

Trends in Mathematics, 2015

Research paper thumbnail of Study on the station keeping maintenance for the tpf mission

In 1995, Mayor and Queloz [a] detected for the first time a planet orbiting a nearby star (15.4 p... more In 1995, Mayor and Queloz [a] detected for the first time a planet orbiting a nearby star (15.4 parsecs). Since then, the interest in the detection of extra-solar planets, in order to learn about the origin, evolution, and composition of planetary systems, has grown tremendously and ...

Research paper thumbnail of Dynamics in the Center Manifold around Equilibrium Points in Periodically-Perturbed Three-body Problems

A new application of the parameterization method is presented to compute invariant manifolds abou... more A new application of the parameterization method is presented to compute invariant manifolds about the equilibrium points of Periodically Perturbed Three-Body Problems (PPTBP). These techniques are applied to obtain high-order semi-numerical approximations of the center manifolds about the points L 1,2 of the Sun-perturbed Earth-Moon Quasi-Bicicular Problem (QBCP), which is a particular case of PPTBP. The quality of these approximations is compared with results obtained using equivalents of previous normal form procedures. Then, the parameterization is used to initialize the computation of Poincaré maps, which allow to get a qualitative description of the periodically-perturbed dynamics near the equilibrium points.

Research paper thumbnail of Low-energy trajectory design and autonomous navigation to flyby near-Earth asteroids using CubeSats

In response to the current interest in CubeSats and potential applications for planetary explorat... more In response to the current interest in CubeSats and potential applications for planetary exploration, this work studies the feasibility of using autonomous CubeSats to flyby near-Earth asteroids. Considering the limited performance of current propulsion systems for CubeSats, low-energy (impulsive and low-thrust) trajectories are designed to encounter near-Earth asteroids in the medium-fidelity Circular Restricted Three-Body Problem, and their existence in a high-fidelity ephemeris model is also verified. The use of large ground antennas for deep-space communications might represent a major portion of CubeSat mission budgets, and thus the feasibility of performing optical navigation to autonomously estimate and correct the trajectory of the CubeSat is also evaluated through Monte Carlo simulations. Preliminary results show that approximately 4 asteroids per year could be reached by a 3U CubeSat if deployed around the first or second Sun-Earth Lagrange points. According to the limited...

Research paper thumbnail of Astrodynamics Network AstroNet-II

AstroNet-II has been the European Research Training Network that has trained through research eig... more AstroNet-II has been the European Research Training Network that has trained through research eighteen young scientist and engineers on a number of problems in astrodynamics, all of them of current interest to space agencies and industry. Fourteen partners composed the network, eight of them university departments and research institutes, and the remaining six aerospace companies and space agencies. During its execution (2012-2015) AstroNet-II has been coordinated by the Institut d'Estudis Espacials de Catalunya (IEEC) in Barcelona (www.ieec.cat). The network has organized four Training Schools, open to young researchers not enrolled in AstroNet-II, in which the following short courses were given by some of the best specialist in the field: An introduction in which the following short courses were given by some of the best specialist in the field: An introduction to Differential Algebra, An introduction to MATLAB®/SIMULINK®

Research paper thumbnail of Global analysis of direct transfers from Lunar orbits to Sun-Earth libration point regimes

Celestial Mechanics and Dynamical Astronomy, 2021

In this paper we look forward to obtain a global picture of simple transfer opportunities from Lu... more In this paper we look forward to obtain a global picture of simple transfer opportunities from Lunar to Sun-Earth libration orbits, useful for a preliminary design of these mission scenarios. Considering the trajectory of the Chinese Change’2 spacecraft as a reference case, the main transfer families are characterized and classified. In a second step, the results are analyzed and extended to departures from more general families of orbits about the Moon. Finally, we also include a preliminary sensitivity analysis of the first transfer correction maneuver (TCM1) to cancel injection errors. The methodology is of general applicability to the transfer analysis involving libration point final orbits in other general multi-body restricted systems.

Research paper thumbnail of Systematic study of the dynamics about and between the Libration Points of the Sun-Earth-Moon System

A new approach is proposed for systematic detection and refinement of natural connections EML12 o... more A new approach is proposed for systematic detection and refinement of natural connections EML12 of the Earth-Moon system and SEML12 of Sun-Earth-Moon. It is structured around the Quasi-Bircircular Problem, a restricted coherent and periodic four-body dynamical model of the Sun-Earth-Moon system. The dynamics about the Libration points are described by high-order periodic semi-analytical expansions obtained via the parametrization method.

Research paper thumbnail of Rotation–translation coupling analysis on perturbed spacecraft relative translational motion

Nonlinear Dynamics, 2020

This paper explores an accurate and complete spacecraft six-degrees-of-freedom coupled relative m... more This paper explores an accurate and complete spacecraft six-degrees-of-freedom coupled relative motion model using the dual quaternion representation. Based on this technique, we build a scheme capable of describing both kinematic and dynamic coupling effects on the spacecraft relative translational motion through a further combination with the chaser's precise absolute translational and rotational dynamics. This new model generalizes the existing nonlinear spacecraft relative translational model to include both the kinematic coupling effect due to the displacements of selected feature points relative to the spacecraft centers of mass and the dynamic coupling effect induced by the gravity gradient torque and the orbital perturbations. Several numerical simulations are implemented to validate the

Research paper thumbnail of Analysis of Jet Transport-Based Geostationary Trajectory Uncertainty Propagation

Journal of Guidance, Control, and Dynamics, 2020

This paper investigates an accurate and efficient nonlinear method for propagating geostationary ... more This paper investigates an accurate and efficient nonlinear method for propagating geostationary trajectory uncertainties under four dominant perturbations: solar radiation pressure, Earth's non-spherical gravity potential, and luni-solar gravitational attractions. A Jet Transport-based scheme (also known as Differential Algebra) is considered and implemented in several coordinate representations, and in two forms: Taylor and Chebyshev expansions. Taking into account the size of the uncertainty neighborhood, as well as the order and time

Research paper thumbnail of High-fidelity trajectory design to flyby near-Earth asteroids using CubeSats

Acta Astronautica, 2019

Fast development of CubeSat technology now enables the first interplanetary missions. The potenti... more Fast development of CubeSat technology now enables the first interplanetary missions. The potential application of CubeSats to flyby near-Earth asteroids is explored in this paper in consideration of CubeSats' limited propulsive capabilities and systems constraints. Low-energy asteroid flyby trajectories are designed assuming a CubeSat is initially parked around to the Sun-Earth Lagrange points. High-impulse and low-thrust trajectories with realistic thrusting models are computed first in the Circular Restricted Three-Body Problem (CR3BP), and then in a high-fidelity ephemeris model. Analysis in the ephemeris model is used to confirm that trajectories computed in the CR3BP model also exist in a more realistic dynamical model, and to verify the validity of the results obtained in CR3BP analysis. A catalogue of asteroid flyby opportunities between years 2019 and 2030 is provided, with 80 m/s of available ΔV and departure from halo orbits around the first and second Sun-Earth Lagrange points (of similar size to those typically used by scientific missions). Results show that the CR3BP model can serve as an effective tool to identify reachable asteroids and can provide an initial estimation of the ΔV cost in the ephemeris model (with ±15 m/s accuracy). An impulsive maneuver model can also provide an accurate estimation of the ΔV requirement for a CubeSat equipped with a high-impulse thruster (with 4 m/s accuracy), even if its thrust magnitude is small and requires duty cycling; low-thrust ΔV requirements, however, may differ significantly from the impulsive results (±15 m/s).

Research paper thumbnail of A new subdivision algorithm for the flow propagation using polynomial algebras

Communications in Nonlinear Science and Numerical Simulation, 2018

The Jet Transport method has emerged as a powerful tool for the numerical integration of ordinary... more The Jet Transport method has emerged as a powerful tool for the numerical integration of ordinary differential equations; it uses polynomial expansions to approximate the flow map associated to the differential equation in the neighborhood of a reference solution. One of the main drawbacks of the method is that the region of accuracy becomes smaller along the integration. In this paper we introduce a procedure to determine a ball covering the set of given initial conditions that keeps the accuracy of the integration within a selected threshold. The paper gives detailed explanations of the algorithm illustrated with some examples of applicability, as well as a comparison with a previous existing method for the same purpose.

Research paper thumbnail of Relative Dynamics of Charged Spacecraft in a Magnetic Field applied to Formation Flight

Communications in Nonlinear Science and Numerical Simulation, 2019

We consider several charged spacecraft configurations around a leader spacecraft provided with an... more We consider several charged spacecraft configurations around a leader spacecraft provided with an artificial magnetic field. In all configurations the nominal orbits are chosen to be about the relative equilibrium points of the reference model. Using a linear quadratic regulator controller, we find that controllability is possible in most of the cases, and it is strongly related to the stability of the equilibrium point which, in turn, depends on the orbit of the leader and the rotation rate of its magnetic dipole. The dynamical model considered shows a great potential for future formation flying applications since both, the establishment and maintenance of the configurations, can be managed by merely adjusting the charge on the follower spacecraft. No additional control variables are needed.

Research paper thumbnail of Analysis of the relative dynamics of a charged spacecraft moving under the influence of a magnetic field

Communications in Nonlinear Science and Numerical Simulation, 2018

We analyse a dynamical scenario where a constantly charged spacecraft (follower) moves in the vic... more We analyse a dynamical scenario where a constantly charged spacecraft (follower) moves in the vicinity of another one (leader) that follows a circular Keplerian orbit around the Earth and generates a rotating magnetic dipole. The mass of the follower is assumed to be negligible when compared with the one of the leader and they are supposed to be in a high-Earth orbit, so the Lorentz force on the follower due to the geomagnetic field is ignored. With these as

Research paper thumbnail of Jet transport-based nonlinear state and parameter estimation for geostationary spacecraft

Acta Astronautica, 2019

Based on the jet transport technique, this paper proposes a novel nonlinear Kalman filter for sim... more Based on the jet transport technique, this paper proposes a novel nonlinear Kalman filter for simultaneously estimating the spacecraft state vector and uncertain parameters, either physically related with the spacecraft or with the measurement procedure. Two different coordinate representations, including Cartesian and hybrid geostationary orbital elements, are exploited in the new nonlinear estimators. The performance and sensitivity analyses of the proposed jet transport-based nonlinear estimators are assessed by numerical simulations and compared with the classical extended Kalman filter.

Research paper thumbnail of Invariant manifolds of a non-autonomous quasi-bicircular problem computed via the parameterization method

Nonlinearity, 2017

A new application of the parameterization method is presented to compute invariant manifolds abou... more A new application of the parameterization method is presented to compute invariant manifolds about the libration points of the Sun-Earth-Moon system. The Sun-Earth-Moon environment is modeled by the so-called Quasi-Bicircular Model (qbcp), which is a coherent restricted four-body model that describes the motion of a spacecraft under the simultaneous gravitational influence of the Earth, the Moon, and the Sun. This model can alternatively be seen as a Sun-perturbed Earth-Moon system or a Moon-perturbed Sun-Earth system, both being periodically-perturbed restricted three-body problems (pptbp). The recent parameterization method is applied to obtain high-order, time-dependent, semi-analytical approximations of the center manifolds about the points L 1,2 of these two pptbps. These approximations are then used to initialize the computation of Poincaré maps, which allow to get a qualitative description of the periodically-perturbed dynamics near the equilibrium points. It is shown that, with this new approach, the semi-analytical description of the center manifolds in a coherent four-body environment is valid in a neighborhood significant enough to be used in practice. In particular, the well-known Halo orbit bifurcation is recovered in all cases.