Related papers: A Novel Orbit Parameterization in Spherical Coordi…
Quantum particles, such as spins, can be used for communicating spatial directions to observers who share no common coordinate frame. We show that if the emitter's signals are the orbit of a group, then the optimal detection method may not…
Images of both rotating celestial bodies (e.g., asteroids) and spheroidal planets with banded atmospheres (e.g., Jupiter) can contain features that are well-modeled as a circle of latitude (CoL). The projections of these CoLs appear as…
This paper presents a mathematical model to simulate the trajectory of a meteor as seen by a single observer located anywhere on Earth. Our strategy is to define a new coordinate system, called Radiant Coordinate System, which is centered…
We discuss a new class of coordinate systems for a plane, which provide an analytical representation of arbitrary straightline, and then define the form of potential on the plane, under which the equations of motion of a mass point are…
The finest state space resolution that can be achieved in a physical dynamical system is limited by the presence of noise. In the weak-noise approximation the neighborhoods of deterministic periodic orbits can be computed as distributions…
Bifurcations of periodic orbits as an external parameter is varied are a characteristic feature of generic Hamiltonian systems. Meyer's classification of normal forms provides a powerful tool to understand the structure of phase space…
Radar odometry estimation has emerged as a critical technique in the field of autonomous navigation, providing robust and reliable motion estimation under various environmental conditions. Despite its potential, the complex nature of radar…
Straight lines are common features in human made environments, which makes them a frequently explored feature for control applications. Many control schemes, like Visual Servoing, require the 3D parameters of the features to be estimated.…
Position uncertainty (delocalization) measures for a particle on the sphere are proposed and illustrated on several examples of states. The new measures are constructed using suitably the standard multiplication angle operator variances.…
In this letter, we demonstrate that previously proposed improved state parameterizations for soft and continuum robots are specific cases of Clarke coordinates. By explicitly deriving these improved parameterizations from a generalized…
We propose a quantum interferometric protocol that leverages spin-dependent spatial displacements to enable high-precision parameter estimation beyond classical limits. By inducing a unitary coupling between a particles spin degree of…
It is believed that some numerical technique must be employed for the determination of the system parameters of a visual binary or a star with a planet because the relevant equations are not only highly nonlinear but also transcendental…
Many flexible parameterizations exist to represent data on the sphere. In addition to the venerable spherical harmonics, we have the Slepian basis, harmonic splines, wavelets and wavelet-like Slepian frames. In this paper we focus on the…
We present a novel empirical method for correcting asteroid phase curves for rotational and geometrical effects using precomputed spin-and-shape models. Our approach normalizes sparse photometric data to a pole-on geometry, enabling…
We describe how orbital graphs can be used to improve the practical performance of many algorithms for permutation groups, including intersection and stabilizer problems. First we explain how orbital graphs can be integrated in partition…
We present the notion of orbit decidability into a more general framework, exploring interesting generalizations and variations of this algorithmic problem. A recent theorem by Bogopolski-Martino-Ventura gave a renovated protagonism to this…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
Small satellite systems enable whole new class of missions for navigation, communications, remote sensing and scientific research for both civilian and military purposes. As individual spacecraft are limited by the size, mass and power…
Isothermic parameterizations} are synonyms of isothermal curvature line parameterizations, for surfaces immersed in Euclidean spaces. We provide a method of constructing isothermic coordinate charts on surfaces which admit them, starting…
Particle swarm optimisation is a metaheuristic algorithm which finds reasonable solutions in a wide range of applied problems if suitable parameters are used. We study the properties of the algorithm in the framework of random dynamical…