Related papers: Numerical-analytical Algorithm for Constructing th…
An interesting phenomenon that occurs in projectile motion, the "coming and going", is analyzed considering linear air resistance force. By performing both approximate and numerical analysis, it is showed how a determined critical angle and…
In this paper, trajectory prediction and control design for a desired hit point of a projectile is studied. Projectiles are subject to environment noise such as wind effect and measurement noise. In addition, mathematical models of…
The main goal of the present research is to make a summary of analytical equations that can be found to calculate a swing-by maneuver in the three-dimensional space. Analytical equations based in the patched conics approximation are showed…
The study focuses on propagation of longitudinal waves in an elastic pipe partly embedded in a medium with dry friction. Mathematical formulation of the problem on the impact pipe driving into the soil is based on the model of longitudinal…
Projectile motion is one of the most fundamental problems in introductory physics, offering a clear context to connect algebraic reasoning with conceptual understanding. This work presents a computational and pedagogical framework that…
Methods are presented for measuring thrust using common force sensors and data acquisition to construct a dynamic force plate. A spreadsheet can be used to compute trajectory by integrating the equations of motion numerically. These…
Broadening is a classic jet observable that probes the transverse momentum structure of jets. Traditionally, broadening has been measured with respect to the thrust axis, which is aligned along the (hemisphere) jet momentum to minimize the…
We develop a unified scattering approach to dynamical Casimir problems which can be applied to both accelerating boundaries, as well as dispersive objects in relative motion. A general (trace) formula is derived for the radiation from…
Based on the double pendulum and Lagrange equation, the moving particles are captured by a binocular three-dimensional capture camera. Two trajectory models of Astrojax and the relationship between trajectory empirical formula and…
This paper presents an analysis of optimal impact strategies to deflect potentially dangerous asteroids. To compute the increase in the minimum orbit intersection distance of the asteroid due to an impact with a spacecraft, simple…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider orbital motion in transverse plane for a single…
We study multiple elastic collisions of a block and a ball against a rigid wall in one dimension. The complete trajectory of the block is solved as an analytic function of time. Near the turning point of the block the force carried by the…
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…
The underlying physics of basketball shooting seems to be a straightforward example of the Newtonian mechanics that can easily be traced by numerical methods. However, a human basketball player does not make use of all the possible…
In this study a new approach is proposed for the generation of aircraft trajectories. The relative guidance of an aircraft, which is aimed to join in minimum time the track of a leader aircraft, is particularly considered. In a first place,…
We study the minimum time control problem of the launchers. The optimal trajectories of the problem may contain singular arcs, and thus chattering arcs. The motion of the launcher is described by its attitude kinematics and dynamics and…
In the following paper a version of the classical Mahler formula is found. The height and the measure are now relative to a self-map on a projective space of arbitrary dimension.
In this paper, we consider a satellite orbiting in a Manev gravitational potential under the influence of an atmospheric drag force that varies with the square of velocity. Using an exponential atmosphere that varies with the orbital…
We present an analysis on the geometrical place formed by the set of maxima of the trajectories of a projectile launched in a media with linear drag. Such a place, the locus of apexes, is written in term of the Lambert $W$ function in polar…
The problem of a disc and a ball rolling on a horizontal plane without slipping is considered. Differential constrained equations are shown to be integrated when the trajectory of the point of contact is taken in a form of the natural…