Related papers: Numerical-analytical Algorithm for Constructing th…
The design of mission scenarios for the flyby investigation of nearby star systems by probes launched using directed energy is addressed. Multiple probes are launched with a fixed launch infrastructure, and download of scientific data…
In this paper the exact analytical solution of the motion of a rigid body with arbitrary mass distribution is derived in the absence of forces or torques. The resulting expressions are cast into a form where the dependence of the motion on…
When modeling the three-dimensional hydrodynamics of interstellar material rotating in a galactic gravitational potential, it is useful to have an analytic expression for gravitational perturbations due to stellar spiral arms. We present…
This paper presents a general formulation of equations of motion of a pendulum with n point mass by use of two different methods. The first one is obtained by using Lagrange Mechanics and mathematical induction(inspection), and the second…
A method is proposed for the determination of the position and inclination angles of the plane of a spiral galaxy based on the assumption that every spiral arm is a monotonic function of the radius versus azimuthal angle. This method may…
Performing striking aerobatic flight in complex environments demands manual designs of key maneuvers in advance, which is intricate and time-consuming as the horizon of the trajectory performed becomes long. This paper presents a novel…
We investigate variants of Goddard's problems for nonvertical trajectories. The control is the thrust force, and the objective is to maximize a certain final cost, typically, the final mass. In this report, performing an analysis based on…
A straightforward analytical scheme is proposed for computing the long-time, asymptotic mean velocity and dispersivity (effective diffusivity) of a particle undergoing a discrete biased random walk on a periodic lattice amongst an array of…
In this paper, we consider the dynamics of a heavy homogeneous ball moving under the influence of dry friction on a fixed horizontal plane. We assume the ball to slide without rolling. We demonstrate that the plane may be divided into two…
We consider three problems of selecting optimal gun barrel direction (or those of selecting optimal semiaxis position) when firing an unguided artillery projectile on the assumption that the gun barrel semiaxis can move in a connected…
In this paper, a complexity indicator for 4D flight trajectories is developed based on conflict probability. A 4D trajectory is modeled as piecewise linear segments connected by waypoints. The position of each aircraft is modeled as a 2D…
We consider the problem of relativistic projectiles in a uniform gravitational force field in an inertial frame. For the first time, we have found the curve that joins the points of maximum height of all trajectories followed by a…
In this paper we study the problem of designing periodic orbits for a special class of hybrid systems, namely mechanical systems with underactuated continuous dynamics and impulse events. We approach the problem by means of optimal control.…
We construct an example of a real plane analytic singular metric, degenerating only at the origin, such that any gradient trajectory (respectively to this singular metric) of some well chosen function spirals around the origin. The…
The author considers the planar rotational motion of the mathematical pendulum with its pivot oscillating both vertically and horizontally, so the trajectory of the pivot is an ellipse close to a circle. The analysis is based on the exact…
Modeling has been created for a Space-to-Surface system defined for an optimal trajectory for targeting in terminal phase with avoids an intercepting process. The modeling includes models for simulation atmosphere, speed of sound,…
Under analysis is travel of P-waves in an elastic pipe partly embedded in soil with dry friction. The mathematical formulation of the problem on impact pipe driving in soil is based on the model of axial vibration of an elastic bar,…
We present a simple and efficient acceleration technique for an arbitrary method for computing the Euclidean projection of a point onto a convex polytope, defined as the convex hull of a finite number of points, in the case when the number…
A new dynamic control algorithm in order to direct the trajectory of a glider to a pre-assigned target point is proposed. The algorithms runs iteratively and the approach to the target point is self-correcting. The algorithm is applicable…
We consider a problem on maximizing the height of vertical flight of a material point ("meteorological rocket") in the presence of a nonlinear friction and a constant flat gravity field under a bounded thrust and fuel expenditure. The…