Related papers: A Method for Calculating Collision Probability Bet…
The core of every orbit determination process is the comparison between the measured observables and their predicted values, computed using the adopted mathematical models, and the minimization, in a least square sense, of their…
In this paper, a novel technique for tight outer-approximation of the intersection region of a finite number of ellipses in 2-dimensional (2D) space is proposed. First, the vertices of a tight polygon that contains the convex intersection…
We propose a new scenario for compound chondrule formation named as "fragment-collision model," in the framework of the shock-wave heating model. A molten cm-sized dust particle (parent) is disrupted in the high-velocity gas flow. The…
We present an algorithm to compute the minimum orbital intersection distance (MOID), or global minimum of the distance between the points lying on two Keplerian ellipses. This is achieved by finding all stationary points of the distance…
We present a continuous-time collision detection algorithm for quickly detecting whether certain polynomial trajectories in time intersect with convex obstacles. The algorithm is used in conjunction with an existing multicopter trajectory…
Current and future colliders will provide high precision experimental data. In order to use the high experimental precision it has to be matched with theoretical predictions at the same level of accuracy or better. This involves the…
We present a novel technique to estimate the 6D pose of objects from single images where the 3D geometry of the object is only given approximately and not as a precise 3D model. To achieve this, we employ a dense 2D-to-3D correspondence…
Achieving collision avoidance between moving objects is an important objective while determining robot trajectories. In performing collision avoidance maneuvers, the relative shapes of the objects play an important role. The literature…
Given two distributions $P$ and $S$ of equal total mass, the Earth Mover's Distance measures the cost of transforming one distribution into the other, where the cost of moving a unit of mass is equal to the distance over which it is moved.…
By quantifying the distance between two collider events, one can triangulate a metric space and reframe collider data analysis as computational geometry. One popular geometric approach is to first represent events as an energy flow on an…
The survival probability of large rapidity gaps in pp collisions is calculated for several different eikonal models of the Gaussian form. Results obtained for models based on partonic interactions are quite similar. The Regge-pole model…
We construct a highly-symmetric periodic orbit of eight bodies in three dimensions. In this orbit, each body collides with its three nearest neighbors in a regular periodic fashion. Regularization of the collisions in the orbit is achieved…
We present a procedure for determination of positions and orbital elements, and associated uncertainties, of outer Solar System planets. The orbit-fitting procedure is greatly streamlined compared to traditional methods because acceleration…
Generalizing the well-known relations on characteristic functions on a plane to the case of a one-dimensional regular surface (curve) with compact support, we establish implicit equations for these functions. Introducing an approximation,…
We investigate the distribution of encounter velocities and impact angles describing collisions in the habitable zone of the early planetary system. Here we present a catalogue of collision characteristics for a particular mass ratio of the…
We study the time evolution of the impact probability for synthetic but realistic impacting and close approaching asteroids detected in a simulated all-sky survey. We use the impact probability to calculate the impact warning time as the…
In this study, we conducted an experiment to estimate $\pi$ using body-to-body and body-to-wall collisions. By geometrically analyzing the system's motion, we first review how the collision count corresponds to the digits of $\pi$. This…
Estimating the probability of failures or accidents with aerospace systems is often necessary when new concepts or designs are introduced, as it is being done for Autonomous Aircraft. If the design is safe, as it is supposed to be, accident…
Neglecting small fragments in space debris evolutionary models can lead to a significant underestimation of the collision risk for operational satellites. However, when scaling down to the millimeter range, the debris population grows to…
We introduce a new event shape observable -- event isotropy -- that quantifies how close the radiation pattern of a collider event is to a uniform distribution. This observable is based on a normalized version of the energy mover's…