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It is attempted to derive the general relativistic (GR) equation of motion for planet and its solution solely by the special relativity (SR) techniques. The motion of a planet relative to the sun and that of the sun to the planet are solved…
The main motivation of this research is the analytical exploration of the dynamics of asteroid rotation when it moves in elliptic orbit through Space. According to the results of Efroimsky, Frouard (2016), various perturbations (collisions,…
Generalizable manipulation requires that robots be able to interact with novel objects and environment. This requirement makes manipulation extremely challenging as a robot has to reason about complex frictional interaction with uncertainty…
This paper presents an integrated model-learning predictive control scheme for spacecraft orbit-attitude station-keeping in the vicinity of asteroids. The orbiting probe relies on optical and laser navigation while attitude measurements are…
An alternative numerical method is developed to find stable and unstable periodic orbits of nonlinear dynamical systems. The method exploits the high-efficiency of the Levenberg-Marquardt algorithm for medium-sized problems and has the…
When rotation is not taken into account, the measurement of the Gravitational Redshift can provide unique information about the compactness ($M/R$) of the star. Rotation alters the gravitational redshift rendering thereby a unique…
This paper considers the analysis of continuous time gradient-based optimization algorithms through the lens of nonlinear contraction theory. It demonstrates that in the case of a time-invariant objective, most elementary results on…
This paper presents a novel trajectory optimization formulation to solve the robotic assembly of the belt drive unit. Robotic manipulations involving contacts and deformable objects are challenging in both dynamic modeling and trajectory…
In this paper, a dynamic-programming approach to the coupled translational and rotational control of thruster-driven spacecraft is studied. To reduce the complexity of the problem, dynamic-programming-based optimal policies are calculated…
In Epoch 2 of the 2024 PDC25 Hypothetical Asteroid Impact Scenario, an asteroid is confirmed to be on a collision course with the Earth, and its size and surface composition have been well characterized via a flyby mission. A kinetic…
We proposed a gravitation theory based on an analogy with electrodynamics on the basis of a vector field. For the first time, to calculate the basic gravitational effects in the framework of a vector theory of gravity, we use a Lagrangian…
In this thesis, I investigate how to construct a self-consistent model of deformed general relativity using canonical methods and metric variables. The specific deformation of general covariance is predicted by some studies into loop…
Recently, we proposed a novel charged wormhole spacetime based on Yoshiaki Sofue's exponential dark matter density profile, referred to as the Charged Galactic Wormhole. Our previous work explored the deflection of light and massive…
We present a fast trajectory optimization algorithm for the soft capture of uncooperative tumbling space objects. Our algorithm generates safe, dynamically feasible, and minimum-fuel trajectories for a six-degree-of-freedom servicing…
Asteroid mining can become an enabling technology to establish a sustainable manned colony on Mars, which requires metallic materials more often than they are readily available in shipments from Earth. This paper describes a feasibility…
We consider many-body problems in classical mechanics where a wide range of time scales limits what can be computed. We apply the method of optimal prediction to obtain equations which are easier to solve numerically. We demonstrate by…
The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…
We have presented in this communication a new solving procedure for the dynamics of non-rigid asteroid rotation, considering the final spin state of rotation for a small celestial body (asteroid). The last condition means the ultimate…
The maximum strength of gravity at the surface of an object of a given mass is not attained for a spherical shape, but for a small departure from sphericity.
This paper addresses an optimal control problem for a robot that has to find and collect a finite number of objects and move them to a depot in minimum time. The robot has fourth-order dynamics that change instantaneously at any pick-up or…