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The dynamics of compact binary systems at the fourth post-Newtonian (4PN) approximation of general relativity has been recently completed in a self-consistent way. In this paper, we compute the ten Poincar\'e constants of the motion and…
We present a framework for bi-level trajectory optimization in which a system's dynamics are encoded as the solution to a constrained optimization problem and smooth gradients of this lower-level problem are passed to an upper-level…
The classical fuel-optimal two-impulse rendezvous problem between Keplerian orbits is revisited from a family-based perspective. Conventional approaches often yield isolated optimal solutions whose mutual relationships remain unclear; yet,…
The use of four Lagrange points of the Sun/Earth system for fundamental physics experiments in space is presented. L1, L2, L4 and L5 rotating rigidly together with the Earth form a natural reference frame at the scale of the inner solar…
We study the dynamics in the neighborhood of the collinear Lagrangian points in the spatial, circular, restricted three--body problem. We consider the case in which one of the primaries is a radiating body and the other is oblate (although…
A prototype of ion beam transport module has been developed at the Institut Pluridisciplinaire Hubert Curien (IPHC) and used as a test bed to investigate key issues related to the efficient transport of ion beams. This includes the…
Deterministically solving charged particle transport problems at a sufficient spatial and angular resolution is often prohibitively expensive, especially due to their highly forward peaked scattering. We propose a model order reduction…
This paper proposes a systematic method for generating practical and robust low-thrust spacecraft trajectories. One contribution is to consider the change in mass of the spacecraft at two levels: a) the propulsive acceleration and b) the…
Many science missions require an unobstructed view of space and a stable thermal environment but lack the technical or programmatic resources to reach orbits that satisfy these needs. This paper presents a high Earth orbit in 2:1 resonance…
Consider the Restricted Planar Circular Three Body Problem (RPC3BP), which models the motion of a massless particle (Asteroid) under the gravitational influence of two massive bodies (the primaries) moving on circular orbits. By considering…
Transiting planets manifest themselves by a periodic dimming of their host star by a fixed amount. On the other hand, light curves of transiting circumbinary (CB) planets are expected to be neither periodic nor to have a single depth while…
Growing penetration of renewable generation in power systems brings more challenges in transient stability assessment using direct methods. One of the reasons is the inability to assess the risk of instability brought by tripping of a large…
Reachability analysis plays a central role in low-thrust spacecraft trajectory optimization by identifying which target states can be achieved under constraints on time, thrust, and propellant. Classical approaches construct reachable sets…
We investigate the possibility of calculating the parameters of few-body resonances using the oscillator trap boundary conditions. We place the few-body system in an oscillator trap and calculate the energy spectrum and the strength…
The $N$-body problem is of historical significance because it was the first implementation of the Newtonian dynamical laws for the description of our Solar System. Motivated by this, the project's goal is to revisit this problem for small…
This paper explores the benefits of computing arborescent trajectories (trajectory-trees) instead of commonly used sequential trajectories for partially observable robotic planning problems. In such environments, a robot infers knowledge…
We start by reviewing our previous work on retrograde orbital configurations and on modeling and identifying retrograde resonances. Then, we present new results regarding the enhanced stability of retrograde configurations with respect to…
A method for generating unsupervised conditional mapping rules for multi-inter-corridor transfer limits and their integration into unit commitment through banding-switching is proposed in this paper. The method starts by using Ant colony…
This work presents a new method for generating impulsive trajectories in restricted two-body systems by leveraging Riemannian geometry. The proposed method transforms the standard trajectory optimization problem into a purely geometric one…
In its most general form, the optimal transport problem is an infinite-dimensional optimization problem, yet certain notable instances admit closed-form solutions. We identify the common source of this tractability as \textit{symmetry} and…