Related papers: Study of the projectile motion in the air using si…

The use of compressed air cannons in an undergraduate lab provides a way to illustrate the cooperation of diverse physics concepts, such as conservation of momentum, the work-kinetic energy theorem, expansion of gas, air drag, and…

Several scenarios used in teaching feature a rolling motion with slipping that transitions to one without through friction with the ground. We summarise these transitions by introducing an unknown impulse that is transferred to the ground.…

We examine the motion of a relativistic charged particle in a constant magnetic field perturbed by gravitational waves incident along the direction of the magnetic field. We apply a generalized energy conservation law to compute the…

We introduce a simple framework for learning aggressive maneuvers in flight control of UAVs. Having inspired from biological environment, dynamic movement primitives are analyzed and extended using nonlinear contraction theory. Accordingly,…

Nonlinear dynamics of a bouncing ball moving in gravitational field and colliding with a moving limiter is considered. Displacement of the limiter is a quadratic function of time. Several dynamical modes, such as fixed points, 2 - cycles…

Constraints imposed directly on accelerations of the system leading to the relation of constants of motion with appropriate local projectors occurring in the derived equations are considered. In this way a generalization of the Noether's…

Relativistically covariant form of equation of motion for real particle (neutral in charge) under the action of electromagnetic radiation is derived. Various formulations of the equation of motion in the proper frame of reference of the…

The project consists to determine, mathematically, the trajectory that will take an artificial satellite to fight against the air resistance. During our work, we had to consider that our satellite will crash to the surface of our planet. We…

Let a number, N, of particles interact classically through Newton's Laws of Motion and Newton's inverse square Law of Gravitation. The resulting equations of motion provide an approximate mathematical model with numerous applications in…

We present a perturbation theory by extending a prescription due to Feynman for computing the probability density function for the random flight motion. The method can be applied to a wide variety of otherwise difficult circumstances. The…

We analyze the frictionless motion of a point-like particle that slides under gravity on an inverted conical surface. This motion is studied for arbitrary initial conditions and a general relation, valid within 13%, between the periods of…

Modeling of a wide class of physical phenomena, such as crystal growth and flame propagation, leads to tracking fronts moving with curvature-dependent speed. When the speed is the curvature this leads to one of the classical degenerate…

A new explanation for space contraction and time dilation in special relativity is offered based on kinetic energy differences between observers rather than velocity differences. The classical (Newtonian) concept of projectile motion…

We study the problem of minimal resistance for a body moving with constant velocity in a rarefied medium of chaotically moving point particles, in Euclidean space R^d. The particles distribution over velocities is radially symmetric. Under…

Contraction analysis considers the distance between two adjacent trajectories. If this distance is contracting, then trajectories have the same long-term behavior. The main advantage of this analysis is that it is independent of the…

We present an analytical solution for the projectile coplanar motion under constant drag parametrised by the velocity angle. We found the locus formed by the apices of the projectile trajectories. The range and time of flight are obtained…

Motion of a point particle sliding on a turntable is studied. The equations of motion are derived assuming that the table exerts frictional force on the particle, which is of constant magnitude and directed opposite to the direction of…

The anomalous velocity deviation in the osculating planetary flyby attracts enough attention as a problem of General Relativity. In connection of rotating weak field massive source the Lense Thirring metric is diagonalized to find the…

We consider the periodic Manhattan lattice with alternating orientations going north-south and east-west. Place obstructions on vertices independently with probability $0<p<1$. A particle is moving on the edges with unit speed following the…

Arithmetic dynamics is the study of number theoretic properties of dynamical systems. A relatively new field, it draws inspiration partly from dynamical analogues of theorems and conjectures in classical arithmetic geometry, and partly from…