The paper presents the exact solution to the relative orbital motion that takes place in a central force field. This problem is a generalization of the problem of the Keplerian relative motion in a central force field. The solution is presented in a coordinate free vectorial form, offering closed form expressions for the law of motion and the velocity. The solution is offered to the non-linear model of the relative motion problem, and it generalizes

A direct application of Kepler’s problem in rotating reference frames is the orbital relative motion study. The nonlinear differential equation modeling the motion is solved by means of tensorial and vectorial regularization methods. The general framework for obtaining exact solutions to the relative orbital motion is given when the reference trajectory is elliptic, parabolic, and hyperbolic. All the results are presented in a vectorial closed

This paper studies the Keplerian motion in rotating reference frames based on tensorial orthogonal and skewsymmetric maps. By using a time-regularization vectorial method, an exact solution to Keplerian noninertial motion is offered. A qualitative and quantitative comprehensive study is made. The paper generalizes the approaches to the inertial Keplerian motion presented by Levi-Civita and Kustaanheimo–Stiefel. A Sundman-like vectorial regularization

The present paper shows that various matrix expressions for the solution to the relative orbital motion may be written in a much simpler form, which was introduced for the first time in [6,7]. Instead of using the orbital elements as constants of motion, this novel approach is based on a tensorial frame-independent form of the solution to the relative orbital dynamics. The results deduced in the case of the relative spacecraft motion in a gravitational

The paper gives an exact vectorial solution to the Kepler problem. A vectorial regularization that linearizes the Kepler problem is given using a Sundman transformation. Closed form expressions describing the Keplerian motion are deduced. A unified approach to the classic Kepler problem is offered, by studying both rectilinear and non-rectilinear Keplerian motions with the same instrument. The approach is an elementary one and only simple vectorial

The paper offers a comprehensive study of the motion in a central force field with respect to a rotating non-inertial reference frame. It is called Foucault Pendulum-like motion and it is a generalization of a classic Theoretical Mechanics problem. A closed form vectorial solution to this famous problem is presented. The vectorial time-explicit solution for the classic Foucault Pendulum problem is obtained as a particular case of the considerations

The present work presents an approach to the relative orbital motion by using hypercomplex numbers. An extension to this notion is used for vectors, by introducing the hypercomplex vector in the same way as hypercomplex numbers are defined. The solution to the relative orbital motion is offered in all possible situations (it stands for any Keplerian reference or targeted trajectories). A unified view on the relative orbital motion is suggested, by

The paper offers a vectorial approach to the J2-perturbed relative orbital motion. The model uses mean orbital elements in order to derive closed form expressions for the relative position and relative velocity with respect to the LVLH frame attached on a main satellite. The advantage of the present approach is that only the motion of one satellite must be known, together with the initial conditions with respect to LVLH of the other satellites. As

This paper studies the relative orbital motion between arbitrary Keplerian trajectories. A closed-form vectorial solution to the nonlinear initial value problem that models this type of motion with respect to a noninertial reference frame is offered. Without imposing any particular conditions on the leader or the deputy satellites trajectories, exact expressions for the relative law of motion and relative velocity are obtained in a closed form. This

The papers o ers new insights of the unperturbed relative orbital motion, by proving that this motion is super-integrable, in the sense that is has the maximum possible number of rst integrals. By using an adequate change of variable, the problem may be reduced to the classic Kepler problem in an inertial frame. Other interesting aspects are presented in this approach: a tensor rst integral of the relative motion, and a Hamiltonian formulation of