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This article describes a bipedal walking algorithm with inverse kinematics resolution based solely on geometric methods, so that all mathematical concepts are explained from the base, in order to clarify the reason for this solution. To do…
We discuss a covariant generalization of the parametrized post-Newtonian (PPN) formalism in a class of scalar-tensor theories of gravity. It includes an exact construction of a set of global and local (Fermi-like) references frames for an…
The regularization of a new problem, namely the three-body problem, using 'similar' coordinate system is proposed. For this purpose we use the relation of 'similarity', which has been introduced as an equivalence relation in a previous…
This paper presents a simple approach to low-thrust optimal-fuel and optimal-time transfer problems between two elliptic orbits using the Cartesian coordinates system. In this case, an orbit is described by its specific angular momentum and…
This paper explores the dynamic properties of the planar system of an ellipsoidal satellite in an equatorial orbit about an oblate primary. In particular, we investigate the conditions for which the satellite is bound in librational motion…
The spacecraft attitude tracking problem is addressed with actuator faults and uncertainties among inertias, external disturbances, and, in particular, state estimates. A continuous sliding mode attitude controller is designed using…
Numerical solutions of Kepler's Equation are critical components of celestial mechanics software, and are often computation hot spots. This work uses symbolic regression and a genetic learning algorithm to find new initial guesses for…
We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…
A trajectory isomorphism between the two Newtonian fixed center problem in the sphere and two associated planar two fixed center problems is constructed by performing two simultaneous gnomonic projections in $S^2$. This isomorphism converts…
The long-term dynamics of the geostationary Earth orbits (GEO) is revisited through the application of canonical perturbation theory. We consider a Hamiltonian model accounting for all major perturbations: geopotential at order and degree…
Two complementary and equally important approaches to relativistic physics are explained. One is the standard approach, and the other is based on a study of the flows of an underlying physical substratum. Previous results concerning the…
This paper introduces a new class of algorithms for solving large-scale linear inverse problems based on new flexible and inexact Golub-Kahan factorizations. The proposed methods iteratively compute regularized solutions by approximating a…
We present a general approach for the formulation of equations of motion for compact objects in general relativistic theories. The particle is assumed to be moving in a geometric background which in turn is asymptotically flat. Our approach…
In the coordinated motion planning problem, we are given a graph together with the starting and destination vertices of $k$ robots. At each time step, any subset of robots may move, each traversing an edge of the graph, provided that no two…
Emission relativistic coordinates are a class of spacetime coordinates defined and generated by four emitters (satellites, pulsars) broadcasting their proper time by radio signals. They are the main ingredient of the simplest conceivable…
In the framework of multi-body dynamics, successive encounters with a third body, even if well outside of its sphere of influence, can noticeably alter the trajectory of a spacecraft. Examples of these effects have already been exploited by…
This work focuses on the generation of non-self-intersecting relative trajectories, and their applications to satellite constellation design, slotting architectures, and Space Traffic Management. To that end, this paper introduces two…
We show that fundamental plane of elliptical galaxies can be used to obtain observational constraints on metric theories of gravity. Being it connected to global properties of ellipticals, it can fix parameters of modified gravity.…
A local positional system (LPS) is proposed, in which particles are launched at given velocities, and a sensor system measures the trajectory of particles in the platform frame. These measurements allow us to restore the position and…
Three parameterizations are developed for modeling translational motion of a point mass in atmosphere flight over a central rotating body. Unlike well-known parameterizations such as spherical coordinate parameterizations, where position…