Related papers: Lambert's problem in orbital dynamics: a self--con…
Lambert's problem is the orbital boundary-value problem constrained by two points and elapsed time. It is one of the most extensively studied problems in celestial mechanics and astrodynamics, and, as such, it has always attracted the…
The Lambert problem is to determine the gravitational orbit between two points that has a specified time of flight, allowing the second point to be a moving target such as a satellite. After a review of gravitational orbits, a solution of…
The Lambert problem consists in connecting two given points in a given lapse of time under the gravitational influence of a fixed center. While this problem is very classical, we are concerned here with situations where friction forces act…
The orbital boundary value problem, also known as Lambert Problem, is revisited. Building upon Lancaster and Blanchard approach, new relations are revealed and a new variable representing all problem classes, under L-similarity, is used to…
A fundamental problem in spacecraft mission design is to find a free flight path from one place to another with a given transfer time. This problem for paths in a central force field is known as Lambert's problem. Although this is an old…
The Lambert problem originated in orbital mechanics. It concerns with determining the initial velocity for a boundary value problem involving the dynamical constraint due to gravitational potential with additional time horizon and endpoint…
The deterministic variant of the Lambert's problem was posed by Lambert in the 18th century and its solution for conic trajectory has been derived by many, including Euler, Lambert, Lagrange, Laplace, Gauss and Legendre. The solution…
A numerical approach to solve the perturbed Lambert's problem is presented. The proposed technique uses the Theory of Functional Connections, which allows the derivation of a constrained functional that analytically satisfies the boundary…
You have a satellite spacecraft or asteroid that moves under the gravitational influence of a massive central body and follows a Keplerian orbit around it ellipse parabola or hyperbola Given measurements of two positions in its orbit what…
Lambert's theorem (1761) on the elapsed time along a Keplerian arc drew the attention of several prestigious mathematicians. In particular, they tried to give simple and transparent proofs of it (see our timeline \S 9). We give two new…
A simple mathematical procedure is introduced which allows redefining in an exact way divergent integrals and limits that appear in the basic equations of classical electrodynamics with point charges. In this way all divergences are at once…
We give simple proofs of some simple statements concerning the Lambert problem. We first restate and reprove the known existence and uniqueness results for the Keplerian arc. We also prove in some cases that the elapsed time is a convex…
In Euclidean relational particle mechanics, only relative times, relative angles and relative separations are meaningful. Barbour--Bertotti (1982) theory is of this form and can be viewed as a recovery of (a portion of) Newtonian mechanics…
We prove that the classical Lambert theorem about the elapsed time on an arc of Keplerian orbit extends without change to the Kepler problem on a space of constant curvature. We prove that the Hooke problem has a property similar to…
We give a survey at an introductory level of old and recent results in the study of critical points of solutions of elliptic and parabolic partial differential equations. To keep the presentation simple, we mainly consider four exemplary…
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…
The Bertrand theorem concluded that; the Kepler potential, and the isotropic harmonic oscillator potential are the only systems under which all the orbits are closed. It was never stressed enough in the physical or mathematical literature…
If A and B are two points in the plane, with B lower and to the right of A, then we may consider the trajectory of an object travelling from A to B under the influence of gravity. The search for the trajectory minimising the time taken by…
Herein, we present a canonical form for a natural and necessary generalization of the Lambert W function, natural in that it requires minimal mathematical definitions for this generalization, and necessary in that it provides a means of…
There are known problems of Lorentz-Dirac equation for moving with acceleration charged particle in classical electrodynamics. The model of extended in one dimension particle is proposed and shown that electromagnetic self-interaction can…