# Trajectory

trajectoriesflightpathflight pathdistance a cannonball travelsfall linejet airwayJet routeParabolic trajectorypathpaths
The study of projectile is called ballisticwikipedia
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### Projectile

projectileskinetic kill vehiclekinetic projectile
In classical mechanics, the mass might be a projectile or a satellite.
Mathematical equations of motion are used to analyze projectile trajectory.

### Dynamical system

dynamical systemsdynamic systemdynamic systems
In control theory, a trajectory is a time-ordered set of states of a dynamical system (see e.g. Poincaré map).
If the system can be solved, given an initial point it is possible to determine all its future positions, a collection of points known as a trajectory or orbit.

### Ballistics

ballisticforensic ballisticsballistically
This is the focus of the discipline of ballistics.
A ballistic missile is a missile that is guided only during the relatively brief initial phase of powered flight and the trajectory is subsequently governed by the laws of classical mechanics; in contrast to (for example) a cruise missile which is aerodynamically guided in powered flight like a fixed-wing aircraft.

### Physical object

physical bodyobjectbody
A trajectory or flight path is the path that an object with mass in motion follows through space as a function of time.
A physical body is an enduring object that exists throughout a particular trajectory of space and orientation over a particular duration of time, and which is located in the world of physical space (i.e., as studied by physics).

### Uncertainty principle

Heisenberg uncertainty principleHeisenberg's uncertainty principleuncertainty relation
Trajectory in quantum mechanics is not defined due to Heisenberg uncertainty principle that position and momentum can not be measured simultaneously.
Since the Fourier components were not defined at the classical frequencies, they could not be used to construct an exact trajectory, so that the formalism could not answer certain overly precise questions about where the electron was or how fast it was going.

### Motion

movementMotion (physics)locomotion
A trajectory or flight path is the path that an object with mass in motion follows through space as a function of time.

### Parabola

parabolicparabolic curveparabolic arc
In this simple approximation, the trajectory takes the shape of a parabola.
The best-known instance of the parabola in the history of physics is the trajectory of a particle or body in motion under the influence of a uniform gravitational field without air resistance (for instance, a ball flying through the air, neglecting air friction).

### Isaac Newton

NewtonSir Isaac NewtonNewtonian
The derivation of these was one of the major works of Isaac Newton and provided much of the motivation for the development of differential calculus.
Newton used his mathematical description of gravity to prove Kepler's laws of planetary motion, account for tides, the trajectories of comets, the precession of the equinoxes and other phenomena, eradicating doubt about the Solar System's heliocentricity.

### Force

forcesattractiveelastic force
This agrees with the observed orbits of planets, comets, and artificial spacecraft to a reasonably good approximation, although if a comet passes close to the Sun, then it is also influenced by other forces such as the solar wind and radiation pressure, which modify the orbit and cause the comet to eject material into space.
Thus, the straight line path in space-time is seen as a curved line in space, and it is called the ballistic trajectory of the object.

### Aft-crossing trajectory

In 2005, a new trajectory that an air-launched rocket could take to put satellites into orbit was tested.

### Ephemeris

ephemeridesAstronomical Ephemerisastronomical table
In astronomy and celestial navigation, an ephemeris (plural: ephemerides) gives the trajectory of naturally occurring astronomical objects as well as artificial satellites in the sky, i.e., the position (and possibly velocity) over time.

### Orbit

orbitsorbital motionplanetary motion
For example, it can be an orbit — the path of a planet, asteroid, or comet as it travels around a central mass.
In physics, an orbit is the gravitationally curved trajectory of an object, such as the trajectory of a planet around a star or a natural satellite around a planet.

### Galileo Galilei

GalileoGalileanGalilei
The ideal case of motion of a projectile in a uniform gravitational field in the absence of other forces (such as air drag) was first investigated by Galileo Galilei.
Galileo further asserted that the parabola was the theoretically ideal trajectory of a uniformly accelerated projectile in the absence of air resistance or other disturbances.

### Range of a projectile

rangeballistic tablesengagement range
It will also be shown that the range is 2v_h v_v/g, and the maximum altitude is v_v^2/2g.
The distribution of mass within the projectile can also be important, as an unevenly weighted projectile may spin undesirably, causing irregularities in its trajectory due to the magnus effect.

### Mass

inertial massgravitational massweight
A trajectory or flight path is the path that an object with mass in motion follows through space as a function of time.

### Space

spatialphysical spacereal space
A trajectory or flight path is the path that an object with mass in motion follows through space as a function of time.

### Hamiltonian mechanics

HamiltonianHamilton's equationsHamiltonian dynamics
In classical mechanics, a trajectory is defined by Hamiltonian mechanics via canonical coordinates; hence, a complete trajectory is defined by position and momentum, simultaneously.

### Canonical coordinates

conjugate momentacanonical momentumconjugate momentum
In classical mechanics, a trajectory is defined by Hamiltonian mechanics via canonical coordinates; hence, a complete trajectory is defined by position and momentum, simultaneously.

### Quantum mechanics

quantum physicsquantum mechanicalquantum theory
Trajectory in quantum mechanics is not defined due to Heisenberg uncertainty principle that position and momentum can not be measured simultaneously.

### Satellite

satellitesartificial satelliteartificial satellites
In classical mechanics, the mass might be a projectile or a satellite.

### Asteroid

asteroidsminor bodyMinor Planet
For example, it can be an orbit — the path of a planet, asteroid, or comet as it travels around a central mass.

### Primary (astronomy)

central bodyprimaryprimary body
For example, it can be an orbit — the path of a planet, asteroid, or comet as it travels around a central mass.

### Control theory

controlcontrollercontrol theorist
In control theory, a trajectory is a time-ordered set of states of a dynamical system (see e.g. Poincaré map).

### State-space representation

state spaceState space representationState space (controls)
In control theory, a trajectory is a time-ordered set of states of a dynamical system (see e.g. Poincaré map).

### Poincaré map

Poincaré sectionPoincaré cross-sectionPoincaré recurrence map
In control theory, a trajectory is a time-ordered set of states of a dynamical system (see e.g. Poincaré map).