In physics , a trajectory , also a trajectory , a path or a path (sometimes after the English: orbit) is the course of the space curve along which a body or a point, for example the center of gravity of a rigid body , moves. A macroscopic body, such as a bullet or a ball, is also referred to as the trajectory . In a broader sense, the trajectory is a curve in the n-dimensional phase space .
For bodies that are subject to constraints, the shape of the trajectory is described mathematically by kinematics ; z. B. describes a pendulum an arc. For bodies that are only exposed to external forces, the trajectories result as solutions to systems of differential equations . The investigation of the trajectory as the time-dependent course of the location in a reference system is the subject of kinetics .
- The trajectory of a ground level downed cannonball or a ballistic missile called ballistic curve .
- The trajectory of a natural or artificial celestial body in the gravitational field of a central body or in free space runs on a Kepler orbit . In the case of closed orbits in the solar system or in the galaxy , one speaks more of an orbit . According to the conservation of angular momentum , the path of a body in every central field is a plane curve.
- In a homogeneous magnetic field , charged particles describe spiral paths (helical lines) around the magnetic field lines.
- Due to the law of inertia , the trajectory of a body runs straight when there is no force acting on it or there is an equilibrium of forces .
- In road construction, the transition between a straight line and a circle is made in the form of a clothoid .
- In racing, the ideal line is the trajectory of a fixed point on the vehicle on which a section of the route can be driven at the greatest speed.
- The Bohr model describes the trajectory of the electrons around the nucleus as a closed circular paths .
- The meteorology knows the trajectory of a (hypothetical) air particle. A distinction is made between backward and forward trajectories. The former indicate where the air came from, the latter where it is going. Of the trajectory which is streamlined to distinguish; only in a steady flow do trajectories and streamlines coincide.
- In object tracking , a trajectory is represented as the movement path of an object through the temporal sequence of coordinates during the runtime.
- In technical chemistry , trajectories are used to describe the dynamic behavior of a chemical reaction. For this purpose, representations in the so-called state or phase level are used, in which the instantaneous concentration is plotted against the temperature . The trajectories then show the simultaneous change in concentration and temperature during a transition process. Time runs along the trajectory. The graphs can e.g. B. (depending on the starting conditions and of course other variables) have a spiral shape.
- Predator-prey relationships: Lotka-Volterra equations
In the case of visible objects, the trajectory can usually be determined using photographic means, e.g. B. with photogrammetry .
The trajectory of an atomic or subatomic particle is only available as an illustrative aid, since these particles must be described by quantum mechanics . Such particle trajectories can approximately be made visible in bubble or cloud chambers or determined indirectly with hodoscopes or wire chambers .