Related papers: Numerical-analytical Algorithm for Constructing th…
Laboratory experiments on gravitation are usually performed with objects of constant density, so that the analysis of the forces concerns only the geometry of their shape. In an ideal experiment, the shapes of the constituent parts will be…
We describe a method to extract force and diffusion parameters from single trajectories of Brownian particles based on the principle of maximum likelihood. The analysis is well-suited for out-of-equilibrium trajectories, even when a limited…
We perform full 3D numerical simulations of compact objects, such as black holes or neutron stars, boosted through an ambient force-free plasma that posses a uniform magnetization. We study jet formation and energy extraction from the…
Materials that dissipate energy efficiently under high-speed impacts, from micrometeoroid strikes on spacecraft to ballistic penetration in protective systems, are essential for maintaining structural integrity in extreme environments. Yet,…
The flight of a quadcopter drone, readily available as a toy, is analyzed using simple physics concepts. A smartphone with built-in accelerometer and gyroscope was attached to the drone to register the accelerations and angular velocities…
We study a trajectory analysis problem we call the Trajectory Capture Problem (TCP), in which, for a given input set ${\cal T}$ of trajectories in the plane, and an integer $k\geq 2$, we seek to compute a set of $k$ points (``portals'') to…
Despite intensive applications of Navier-Stokes equations in computational-fluid-dynamics (CFD) to understand aerodynamics, fundamental questions remain open since the statistical nature of discrete air molecules with random thermal motion…
Space missions that use low-thrust propulsion technology are becoming increasingly popular since they utilize propellant more efficiently and thus reduce mission costs. However, optimizing continuous-thrust trajectories is complex,…
The motion of atoms and nanoparticles in a trap formed by sequences of counter-propagating light pulses has been analyzed. The atomic state is described by a wave function constructed with the use of the Monte Carlo method, whereas the…
This paper studies a multi-armed bandit (MAB) version of the range-searching problem. In its basic form, range searching considers as input a set of points (on the real line) and a collection of (real) intervals. Here, with each specified…
The method of Hessian measures is used to find the differential equation that defines the optimal shape of nonrotationally symmetric bodies with minimal resistance moving in a rare medium. The synthesis of optimal solutions is described. A…
We develop an original apparatus of the granular impact experiment by which the incident angle of the solid projectile and inclination angle of the target granular layer can be systematically varied. Whereas most of the natural cratering…
In geometric algebra, the rotation of a vector is described using rotors. Rotors are phasors where the imaginary number has been replaced by a oriented plane element of unit area called a unit bivector. The algebra in three dimensional…
The classical theory of plane projective geometry is examined constructively, using both synthetic and analytic methods. The topics include Desargues's Theorem, harmonic conjugates, projectivities, involutions, conics, Pascal's Theorem,…
In this work, we start with a generic mathematical framework for the equations of motion (EOM) in flight mechanics with six degrees of freedom (6-DOF) for a general (not necessarily symmetric) fixed-wing aircraft. This mathematical…
We develop an effective model to describe the dynamics of a system of particle moving in circular configurations around a central mass, by considering the continuum limit of the angular distribution, to obtain the stable configurations for…
The controlled motion of a rolling ball actuated by internal point masses that move along arbitrarily-shaped rails fixed within the ball is considered. Application of the variational Pontryagin's minimum principle yields the ball's…
Mathematical billiards is much like the real game: a point mass, representing the ball, rolls in a straight line on a (perfectly friction-less) table, striking the sides according to the law of reflection. A billiard trajectory is then…
An airplane flying at constant speed and altitude is an example of physics invisible to the pilots and passengers, but visible to remote observers and manifest in the mathematics. The optimum flight path is an arc of a Great Circle,…
Understanding how the release of stored magnetic energy contributes to the generation of non-thermal high energy particles during solar flares is an important open problem in solar physics. Magnetic reconnection plays a fundamental role in…