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We study the spatial isosceles three body problem, which is a system with two degrees of freedom after modulo the rotation symmetry. For certain choices of energy and angular momentum, we find some disk-like global surfaces of section with…
A method to determine the admissibility of symbolic sequences and to find the unstable periodic orbits corresponding to allowed symbolic sequences for the diamagnetic Kepler problem is proposed by using the ordering of stable and unstable…
This paper provides new results for a tracking control of the attitude dynamics of a rigid body. Both of the attitude dynamics and the proposed control system are globally expressed on the special orthogonal group, to avoid complexities and…
Starting with an exact and simple geodesic, we generate approximate geodesics by summing up higher-order geodesic deviations within a General Relativistic setting, without using Newtonian and post-Newtonian approximations. We apply this…
It is attempted to obtain the masses of the celestial bodies, the initial conditions of their motion, and the constant of gravitation, by a global parameter optimization. First, a numerical solution of the N-bodies problem for mass points…
The objective of this paper is to rectify any monocular image by computing a homography matrix that transforms it to a bird's eye (overhead) view. We make the following contributions: (i) we show that the homography matrix can be…
Geometric distortion (GD) critically constrains the precision of astrometry. Using well-established methods to correct GD requires calibration observations, which can only be obtained using a special dithering strategy during the…
The Maxwell equations have a fairly simple form. However, finding solutions of Maxwell's equations is an extremely difficult task. Therefore, various simplifying approaches are often used in optics. One such simplifying approach is to use…
We present an approach for utilizing astrometric orbit information to improve the yield of planetary images and spectra from a follow-on direct detection mission. This approach is based on the notion-strictly hypothetical-that if a…
The problems of point-cloud registration and attitude estimation from vector observations (Wahba's problem) have widespread applications in computer vision and mobile robotics. This work introduces a simple approach for integrating sets of…
In survey series of unknown Earth orbiting objects, no a priori orbital elements are available. In surveys of wide field telescopes possibly many nonresolved object images are present on the single frames of the series. Reliable methods…
The orthogonal beltway problem is the problem of recovering the $\mathrm{O}(n)$-orbit of a $\delta$-function supported at a finite number of points in $\r^n$ from its auto-correlation or, equivalently, second moment. It was introduced as a…
The non-commutative nature of 3D rotations poses well-known challenges in generalizing planar problems to three-dimensional ones, even more so in contact-rich tasks where haptic information (i.e., forces/torques) is involved. In this sense,…
Solution of Ordinary Differential Equation (ODE) model of dynamical system may not agree with its observed values. Often this discrepancy can be attributed to unmodeled forcings in the evolution rule of the dynamical system. In this…
On-board 3D object detection in autonomous vehicles often relies on geometry information captured by LiDAR devices. Albeit image features are typically preferred for detection, numerous approaches take only spatial data as input. Exploiting…
Understanding natural relative motion trajectories is critical to enable fuel-efficient multi-satellite missions operating in complex environments. This paper studies the problem of computing and efficiently parameterizing satellite…
We present a method to detect the unstable periodic orbits of a multidimensional chaotic dynamical system. Our approach allows us to locate in an efficient way the unstable cycles of, in principle, arbitrary length with a high accuracy.…
The design of navigation observers able to simultaneously estimate the position, linear velocity and orientation of a vehicle in a three-dimensional space is crucial in many robotics and aerospace applications. This problem was mainly dealt…
It is well known that a rigid motion of the Euclidean plane can be written as the composition of at most three reflections. It is perhaps not so widely known that a similar result holds for Euclidean space in any number of dimensions. The…
Can a machine or algorithm discover or learn the elliptical orbit of Mars from astronomical sightings alone? Johannes Kepler required two paradigm shifts to discover his First Law regarding the elliptical orbit of Mars. Firstly, a shift…