Trajectile

Feb 28, 2020  Trajectile (Reflect Missle in Europe and Japan) is a puzzle game developed by Q-Games for DSiWare. Nintendo published it in 2009. The game is a puzzle take on the Breakout genre where players aim the projectile's angle and try to destroy the blocks in.

Elements of a trajectoryShells move along ballistic trajectories (Figure 1). In the case of small angles of fall (up to 20°), we speak of shallow trajectories and very low-angle fire; for angles of fall greater than 20°, we speak of steep trajectories and high-angle fire. When fired at airborne targets, antiaircraft shells—unlike artillery shells—have trajectories with only an ascending branch; the trajectories of rocket shells and rocket-assisted projectiles (for example, antitank rockets) have one or more powered phases, in which the rocket engines operate, and several free-flight phases. When the total length of the powered phases is small compared with the whole trajectory, the trajectory differs little from a ballistic trajectory; if the flight is controlled over the entire length of the trajectory or a substantial part of it, the trajectory differs considerably from a ballistic one.

The trajectory of a ballistic missile: ( OA) launch phase, ( AB) insertion phase, ( BK) guided phase, ( KD) segment outside the atmosphere, ( DC) atmospheric phaseThe trajectories of ballistic missiles have powered and free-flight phases (Figure 2). In the powered phase of a trajectory the specified speed and tilt angle that a ballistic missile should have at the end of this phase are imparted to the missile.

The free-flight phase consists of two segments, a segment outside the atmosphere, in which the missile’s nose cone moves like a freely thrown body, and an atmospheric segment, in which the nose cone is stabilized and approaches the target nose first. The continuous curve described by a point in motion.

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If the trajectory is a straight line, the motion of the point is said to be rectilinear; otherwise, it is said to be curvilinear. The shape of a trajectory of a free material particle depends on the forces acting on the particle, the initial conditions of the motion, and the reference frame used. For a constrained particle the trajectory depends also on the constraints that are imposed ( see CONSTRAINT).For example, a vertical line is the trajectory with respect to the earth (if we neglect its diurnal rotation) of a free particle that is released without an initial velocity and moves under the influence of gravity. If, however, an initial velocity v 0 not directed along the vertical is imparted to the particle, then, in the absence of air resistance, the trajectory is a parabola (Figure 1).

A parabolic trajectoryDepending on the initial velocity, the trajectory of a particle moving in a central gravitational field may be an ellipse, a parabola, or a hyperbola; in special cases, the trajectory may be a straight line or a circle. If we regard the earth’s gravitational field as a central field and neglect atmospheric resistance, then the trajectory of a particle given a horizontally directed initial velocity v 0 near the surface of the earth (Figure 2) is a circle when (orbital velocity), an ellipse when, a parabola when (escape velocity), and a hyperbola when. Here, R is the earth’s radius, g is the acceleration of gravity near the earth’s surface, and the motion is considered with respect to axes that are undergoing translational motion, together with the center of the earth, relative to the stars.In the case of a body, such as a satellite, all the above remarks apply to the trajectory of the body’s center of gravity. If, however, the direction of v 0 is neither horizontal nor vertical and, the trajectory of the particle is an arc of an ellipse; this arc intersects the earth’s surface.

The center of gravity of a ballistic missile has such a trajectory.An example of a constrained particle is a small bob suspended on a string ( see PENDULUM). If the string is deflected from the vertical and released without an initial velocity, the trajectory of the bob is an arc of a circle. If, however, an initial velocity that does not lie in the plane of the string’s deflection is imparted to the bob, the trajectories of the bob may be curves of rather complicated shape that lie on the surface of a sphere; such trajectories are characteristic of a spherical pendulum. In the special case of a conical pendulum, the trajectory of the bob is a circle lying in the horizontal plane.

Types of trajectories in the earth’s gravitational fieldThe trajectories of the points of a rigid body depend on the law of the body’s motion. For a translational motion of the body the trajectories of all its points are identical, but in all other cases the trajectories are generally different for the various points of the body. For example, for an automobile wheel on a rectilinear segment of a road, the trajectory of a point on the wheel’s rim relative to the highway is a cycloid, but the trajectory of the wheel’s center is a straight line. Relative to the automobile’s body, the trajectory of a point on the rim is a circle, but the wheel’s center is a fixed point.The determination of trajectories is important both in theoretical studies and in the solution of many practical problems.

Shooting a cannon at a particular angle with respect to the ground.Here’s an example: Imagine that you fire a cannonball at an angle, as shown in the preceding figure. Given the initial speed of the cannonball and the angle at which it was shot, can you determine how far it will travel?How do you handle the motion of an object shot up at an angle? Because you can always break motion in two dimensions into x and y components, and because gravity acts only in the y component, your job is easy. All you have to do is break the initial velocity into x and y components:These velocity components are independent, and gravity acts only in the y direction, which means that v x is constant; only v y changes with time, using the following equation:v y = v yi + at,.