Related papers: An elementary solution to Lambert's problem
We consider the relativistic generalization of the problem of the "least uncomfortable" linear trajectory from point A to point B. The traditional problem minimizes the time-integrated squared acceleration (termed the "discomfort"), and…
Rules for the transformation of time parameters in relativistic Langevin equations are derived and discussed. In particular, it is shown that, if a coordinate-time parameterized process approaches the relativistic Juttner-Maxwell…
One of the fundamental problems in spacecraft trajectory design is finding the optimal transfer trajectory that minimizes the propellant consumption and transfer time simultaneously. We formulate this as a multi-objective optimal control…
An explicit algorithm for the travelling salesman problem is constructed in the framework of adiabatic quantum computation, AQC. The initial Hamiltonian for the AQC process admits canonical coherent states as the ground state, and the…
By observing the transits of exoplanets, one may determine many fundamental system parameters. I review current techniques and results for the parameters that can be measured with the greatest precision, specifically, the transit times, the…
Flight delay happens every day in airports all over the world. However, systemic investigation in large scales remains a challenge. We collect primary data of domestic departure records from Bureau of Transportation Statistics of United…
The notion of traveling wave, which typically refers to some particular spatio-temporal con- nections between two stationary states (typically, entire solutions keeping the same profile's shape through time), is essential in the…
This paper sets out to explain: 1. Why the speed of light c is a constant and is the maximum speed at which any moving entity can travel. 2. Why time elapsed is different for a moving entity relative to a stationary entity. 3. Why there has…
The Finite Fourier Series (FFS) Shape-Based (SB) trajectory approximation method has been used to rapidly generate initial trajectories that satisfy the dynamics, trajectory boundary conditions, and limitation on maximum thrust…
We study a simple geometric model of transportation facility that consists of two points between which the travel speed is high. This elementary definition can model shuttle services, tunnels, bridges, teleportation devices, escalators or…
We present an efficient and parsimonious algorithm to solve mixed initial/final-value problems. The algorithm optimally limits the memory storage and the computational time requirements: with respect to a simple forward integration, the…
In this paper we consider the mass transport problem in the case of a relativistic cost; we can establish the continuity of the total cost, together with a general estimate about the directions in which the mass can actually move, under…
Particle trajectories in the form of a logarithmic spiral with specified angular time dependence, "ZK spirals," are shown to be analytic solutions for motion in non-central, but simple force power-laws. Each ZK spiral is a particular…
This article produces wave equations and constructs traveling wave solutions that are intimately related to Newton's equations of celestial mechanics. The traveling wave solutions are expressed in ``closed form'' in terms of elementary…
We calculate the parton level cross section for the production of two jets that are far apart in rapidity, subject to a limitation on the total transverse momentum Q_0 in the interjet region. We specifically address the question of how to…
We study the parameterized complexity of the following fundamental geometric problems with respect to the dimension $d$: i) Given $n$ points in $\Rd$, compute their minimum enclosing cylinder. ii) Given two $n$-point sets in $\Rd$, decide…
In cosmological first-order phase transitions, the microscopic interaction of the phase transition fronts with non-equilibrium plasma particles manifests itself macroscopically as friction forces. In general, it is a nontrivial problem to…
In the present work, metrics which lead to projected closed orbits are found by comparing the relativistic differential equation of orbits with the corresponding classical differential equation. Physical and geometrical properties of these…
We propose a conic transformation method to solve the Perspective-Three-Point (P3P) problem. In contrast to the current state-of-the-art solvers, which formulate the P3P problem by intersecting two conics and constructing a degenerate conic…
Parametric path problems arise independently in diverse domains, ranging from transportation to finance, where they are studied under various assumptions. We formulate a general path problem with relaxed assumptions, and describe how this…