Related papers: A Method for Calculating Collision Probability Bet…
Aims: We compare the apparent difference in timing of transiting planets (or eclipsing binaries) that are observed from widely separated locations (parallactic delay). Methods: A simple geometrical argument allow us to show that the…
Fast computational method for Hertzian contact theory is proposed. An incremental formula is introduced to calculate the ellipticity of the contact disk when two elastic bodies are in contact. This method can determine the ellipticity with…
The final sizes, composition, and angular momenta of solid planetary bodies depend on the outcomes of collisions between planetary embryos. The most common numerical method for simulating embryo collisions is to combine a gravity solver…
In this paper we describe an algorithm and deduce the related mathematical formulae that allows the computation of observed fluxes in stellar and planetary systems with arbitrary number of bodies being part of a transit or occultation…
Predicting pedestrians' trajectories is a crucial capability for autonomous vehicles' safe navigation, especially in spaces shared with pedestrians. Pedestrian motion in shared spaces is influenced by both the presence of vehicles and other…
Online planning of collision-free trajectories is a fundamental task for robotics and self-driving car applications. This paper revisits collision avoidance between ellipsoidal objects using differentiable constraints. Two ellipsoids do not…
Cooperative robots can significantly assist people in their productive activities, improving the quality of their works. Collision detection is vital to ensure the safe and stable operation of cooperative robots in productive activities. As…
This article presents and compares four approaches for computing the rotation of a point about an axis by an angle in $\mathbb{R}^3$. We illustrate these methods by computing, by hand, the rotation of point $P=(1,0,1)^T$ about axis…
Group-level behaviour of particles undergoing a velocity jump process with hard-sphere interactions is investigated. We derive $N$-particle transport equations that include the possibility of collisions between particles and apply different…
We discuss the probability distribution of relative speed $\Delta V$ of inertial particles suspended in a highly turbulent gas when the Stokes numbers, a dimensionless measure of their inertia, is large. We identify a mechanism giving rise…
Perturbation techniques can be used as an alternative to supercomputer calculations in calculating gravitational radiation emitted by colliding black holes, provided the process starts with the black holes close to each other. We give a…
Collision detection is a critical functionality for robotics. The degree to which objects collide cannot be represented as a continuously differentiable function for any shapes other than spheres. This paper proposes a framework for…
As a complement to experimental and theoretical approaches, numerical modeling has become an important component to study asteroid collisions and impact processes. In the last decade, there have been significant advances in both…
Space debris is a major threat to the satellite infrastructure. A collision with even small particle, e.g. 1 cm of size, can cause a catastrophic event when the parent body, spacecraft or upper stage, will break up into hundreds of…
Eternal inflation predicts our observable universe lies within a bubble (or pocket universe) embedded in a volume of inflating space. The interior of the bubble undergoes inflation and standard cosmology, while the bubble walls expand…
The density of orbital space debris constitutes an increasing environmental challenge. There are three ways to alleviate the problem: debris mitigation, debris removal and collision avoidance. This paper addresses collision avoidance, by…
We show that two basic mechanical processes, the collision of particles and rolling motion of a sphere on a plane, are intimately related. According to our recent findings, the restitution coefficient for colliding spherical particles…
The distance of closest approach of hard particles is a key parameter of their interaction and plays an important role in the resulting phase behavior. For non-spherical particles, the distance of closest approach depends on orientation,…
This paper discusses a simple theoretical throw model for frontal vehicle-pedestrian collisions. The model is based on the simple assumption that pedestrian movement after impact can be approximated by movement of a mass point. Two methods…
We investigate the probability distribution function of the free flight time and of the number of collisions in a hard sphere gas at equilibrium. At variance with naive expectation, the latter quantity does not follow Poissonian statistics,…