Initially a trajectory — a physical and mathematical concept which designates a way of the movement of a point or a physical body. The term comes from the Latin word "trajectus" that "throw" or "transfer" means. Subsequently the Latin term changed value for "what belongs to the movement", and in other industries by it began to designate the line of movement in space of any object, whether it be an artillery shell or the spaceship.
1. The trajectory is a line in three-dimensional space. In mathematics it represents a set of points through which passed, passes or there will pass a certain material object. This line in itself specifies a way of this object. On it it is impossible to learn about why an object began to move or why its way was bent. But a ratio between forces and parameters of an object allow to calculate a trajectory. At the same time an object has to be much less than the way passed by it. Only in this case it can be considered a material point and to speak about a trajectory.
2. The line of the movement of an object is surely continuous. In mathematics and physics it is accepted to speak about the movement of a free or not free material point. The first is affected only by forces. Not free point is as a result of communications with other points which influence its movement and finally its trace too.
3. For the description of a trajectory of any given material point it is necessary to define a reference system. Systems can be inertial and noninertial, and the trace from the movement of the same object will look differently.
4. Way of the description of a trajectory is radius vector. Its parameters depend on time. To the data necessary for the description of a trajectory, the initial point the radius vector, its length and the direction belong. The end radius vector describes a curve which consists of one or several arches in space. Radius of each arch is extremely important as it allows to define acceleration of an object in a certain point. This acceleration is calculated as private from division of a square of normal speed into radius. That is a=v2/R, where and — acceleration, v – the normal speed, and R-arch radius.
5. A real object practically always is under the influence of any given forces which can initiate its movement, stop it or change the direction and speed. Forces can be both external, and internal. For example, at the movement of the spaceship it is affected by force of an attraction of Earth and other space objects, force of the engine and still a set of factors. They also define a flight trajectory.
6. The ballistic trajectory represents the free movement of an object under the influence of only one gravity. The shell, the aircraft, a bomb and others can be such object. In this case there is neither draft, nor other forces capable to change a trajectory. The ballistics is engaged in this type of the movement.
7. It is possible to make the simple experiment allowing to see how the ballistic trajectory depending on initial acceleration changes. Imagine that you dump a stone from a high tower. If you do not report to a stone initial speed, and just release it, the movement of this material point will be rectilinear down. If you throw it in the horizontal direction, then under the influence of various forces (in this case forces of your throw and gravity) the trajectory of the movement will represent a parabola. In this case rotation of Earth can be not considered.