Trajectory

A trajectory or flight path is the path that a moving object follows through space as a function of time. The object might be a projectile or a satellite. For example. It can be an orbit—the path of a planet, an asteroid or a comet as it travels around a central mass. A trajectory can be described mathematically either by the geometry of the path, or as the position of the object over time.

In control theory a trajectory is a time-ordered set of states of a dynamical system (see e.g. Poincaré map). In discrete mathematics, a trajectory is a sequence of values calculated by the iterated application of a mapping to an element of its source.

Physics of trajectories

A familiar example of a trajectory is the path of a projectile, such as a thrown ball or rock. In a greatly simplified model the object moves only under the influence of a uniform gravitational force field. This can be a good approximation for a rock that is thrown for short distances, for example, at the surface of the moon. In this simple approximation, the trajectory takes the shape of a parabola. Generally, when determining trajectories it may be necessary to account for nonuniform gravitational forces and air resistance (drag and aerodynamics). This is the focus of the discipline of ballistics.

Trajectory (fluid mechanics)

In fluid mechanics, meteorology and oceanography, a trajectory traces the motion of a single point, often called a parcel, in the flow.

Trajectories are useful for tracking atmospheric contaminants, such as smoke plumes, and as constituents to Lagrangian simulations, such as contour advection or semi-Lagrangian schemes.

Suppose we have a time-varying flow field, . The motion of a fluid parcel, or trajectory, is given by the following system of ordinary differential equations:

While the equation looks simple, there are at least three concerns when attempting to solve it numerically. The first is the integration scheme. This is typically a Runge-Kutta, although others can be useful as well, such as a leapfrog. The second is the method of determining the velocity vector, at a given position, , and time, t. Normally, it is not known at all positions and times, therefore some method of interpolation is required. If the velocities are gridded in space and time, then bilinear, trilinear or higher-dimensional linear interpolation is appropriate. Bicubic, tricubic, etc., interpolation is used as well, but is probably not worth the extra computational overhead.

Trajectory (disambiguation)

A trajectory is the path a moving object follows through space.

Types of trajectories include:

Trajectory may also refer to:

In cricket, trajectory is known as flight or loop

In writing, trajectory is an informative discussion (or map) of the various avenues texts can travel as they both affect, and are affected by, the world.