Related papers: An elementary solution to Lambert's problem
In this paper, we study the Lambert-Tsallis function, which is a generalization of the Lambert function with two real parameters. We give a condition on the parameters such that there exists a complex domain touching zero on boundary which…
Gateway will represent a primary logistic infrastructure in cislunar space. The identification of efficient orbit transfers capable of connecting Earth, Moon, and Gateway paves the way for enabling refurbishment, servicing, and utilization…
Computationally tractable methods are developed for centralized goal assignment and planning of collision-free polynomial-in-time trajectories for systems of multiple aerial robots. The method first assigns robots to goals to minimize total…
The problem under consideration is to drive a spatial vehicle to a target at a given final time while minimizing fuel consumption. This is a classical optimal control problem in a deterministic setting. However temporary stochastic failures…
In many mobile robotics scenarios, such as drone racing, the goal is to generate a trajectory that passes through multiple waypoints in minimal time. This problem is referred to as time-optimal planning. State-of-the-art approaches either…
Aircraft and crew are two major resources that ensure the smooth operations of airlines. However, with the anticipated growth in the aviation industry, the crew resource is predicted to be insufficient worldwide and has been one of the…
Travel-time tomography seeks to recover a hidden environment from external measurements generated by propagation through an anomalous region. Standard formulations treat propagation as passive, so the environment influences observations…
The question of how to interpret and compute arrival-time distributions in quantum mechanics remains unsettled, reflecting the longstanding tension between treating time as a quantum observable or as a classical parameter. Most previous…
This paper introduces an algorithm to perform optimal reorientation of a spacecraft during a high speed flyby mission that maximizes the time a certain target is kept within the field of view of scientific instruments. The method directly…
Generating time-optimal, collision-free trajectories for autonomous mobile robots involves a fundamental trade-off between guaranteeing safety and managing computational complexity. State-of-the-art approaches formulate spline-based motion…
This study proposes an analytical Delta-V approximation of short-time transfers based on the linear relative motion and a gradient-based nonlinear programming model of multi-target rendezvous and flyby trajectories. In previous studies, the…
In this note we collect some known facts concerning central projection correspondances and time parametrizations of Kepler problems in Euclidean spaces and on Spheres.
We consider the problem of constrained motion along a conic path under a given external potential function. The model is described as a second-class system capturing the behavior of a certain class of specific quantum field theories. By…
We adapt ideas and concepts developed in optimal transport (and its martingale variant) to give a geometric description of optimal stopping times of Brownian motion subject to the constraint that the distribution of the stopping time is a…
A {\em propagation-dispersion equation} is derived for the first passage distribution function of a particle moving on a substrate with time delays. The equation is obtained as the continuous limit of the {\em first visit equation}, an…
Predicting human mobility patterns has many practical applications in urban planning, traffic engineering, infectious disease epidemiology, emergency management and location-based services. Developing a universal model capable of accurately…
A classic problem of the motion of a point mass (projectile) thrown at an angle to the horizon is reviewed. The air drag force is taken into account with the drag factor assumed to be constant. Analytic approach is used for investigation.…
We present a simple method to obtain the solution of a few orbital problems: the Kepler problem, the modified Kepler problem by the addition of an inverse square potential and linear force.
In the first part of this paper, inspired by the geometric method of Jean-Pierre Marec, we consider the two-impulse Hohmann transfer problem between two coplanar circular orbits as a constrained nonlinear programming problem. By using the…
In this study a new approach is proposed for the generation of aircraft trajectories. The relative guidance of an aircraft, which is aimed to join in minimum time the track of a leader aircraft, is particularly considered. In a first place,…