相关论文: A Simple General Solution for Maximal Horizontal R…
The problem of determining the angle at which a point mass launched from ground level with a given speed is a standard exercise in mechanics. Similar, yet conceptually and calculationally more difficult problems have been suggested to…
Optimum projection angles for achieving maximum horizontal range in throwing and jumping events are considerably less than 45 degrees. This unexpected result arise because an athlete can generate a greater projection velocity at low…
A classic problem of the motion of a projectile thrown at an angle to the horizon in a medium with a quadratic resistance law is studied. An approximate analytical solution of the equations of projectile motion is presented, which has a…
Within the standard framework of quasi-steady flight, this paper derives a speed that realizes the maximal obtainable range per unit of fuel. If this speed is chosen at each instant of a flight plan $h(x)$ giving altitude $h$ as a function…
Projectile motion is a constant theme in introductory-physics courses. It is often used to illustrate the application of differential and integral calculus. While most of the problems used for this purpose, such as maximizing the range, are…
A classic problem of the motion of a projectile thrown at an angle to the horizon is studied. Air resistance force is taken into account with the use of the quadratic resistance law. The action of the wind is also taken into account, which…
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…
A classic problem of the motion of a projectile thrown at an angle to the horizon is studied. Air resistance force is taken into account with the use of the quadratic resistance law. The projectile motion is described analytically with…
We consider the problem of the motion of a projectile thrown vertically upward from a surface. In addition to gravity, the drag force of the medium is taken into account, which is considered a quadratic function of the relative velocity of…
A classic problem of the motion of a point mass (projectile) thrown at an angle to the horizon is reviewed. The air drag force is taken into account with the drag factor assumed to be constant. Analytic approach is used for investigation.…
We propose an optimal control framework for persistent monitoring problems where the objective is to control the movement of mobile agents to minimize an uncertainty metric in a given mission space. For a single agent in a one-dimensional…
The motion of a projectile with horizontal initial velocity V0, moving under the action of the gravitational field and a drag force is studied analytically. As it is well known, the projectile reaches a terminal velocity Vterm. There is a…
This work shows the existence of optimal control laws for persistent monitoring of mobile targets in a one-dimensional mission space and derives explicit solutions. The underlying performance metric consists of minimizing the total…
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 article we revisit the projectile motion assuming a retarding force proportional to the velocity, $\vec{F_r} = -mk\vec{V}$. We obtain an analytical expression for the set of maxima of the trajectories, in Cartesian coordinates,…
The isoperimetric problem asks for the maximum area of a region of given perimeter. It is natural to consider other measurements of a region, such as the diameter and width, and ask for the extreme value of one when another is fixed. The…
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…
In contrast to set-point tracking which aims to reduce the tracking error between the tracker and the reference, tracking-in-range problems only focus on whether the tracker is within a given range around the reference, making it more…
We propose an optimal control framework for persistent monitoring problems where the objective is to control the movement of mobile nodes to minimize an uncertainty metric in a given mission space. For multi agent in a one-dimensional…
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…