trajectory

(noun)

The path of a body as it travels through space.

Related Terms

Examples of trajectory in the following topics:

  • Work

    • Work done by a force ($F$) along a trajectory ($C$) is given as $\int_C \mathbf{F} \cdot d\mathbf{x}$.
    • The sum of these small amounts of work over the trajectory of the point yields the work:
    • where $C$ is the trajectory from $x(t_1)$ to $x(t_2)$.
    • This integral is computed along the trajectory of the particle, and is therefore said to be path-dependent.
    • Calculate "work" as the integral of instantaneous power applied along the trajectory of the point of application

  • Applications of the Parabola

    • The parabolic trajectory of projectiles was discovered experimentally in the 17th century by Galileo, who performed experiments with balls rolling on inclined planes.
    • As in all cases in the physical world, a projectile's trajectory is an approximation.
    • All of the physical examples are situations where an object's trajectory or the shape of an object fits a generalized parabola function:
    • Aircraft used to create a weightless state for purposes of experimentation, such as NASA's "Vomit Comet," follow a vertically parabolic trajectory for brief periods in order to trace the course of an object in free fall, which, for most purposes, produces the same effect as zero gravity.
    • In this image, the water shot from a fountain follows a parabolic trajectory as gravity pulls it back down.

  • Key Points: Range, Symmetry, Maximum Height

    • The path that the object follows is called its trajectory.
    • The path that the object follows is called its trajectory.
    • Projectile motion only occurs when there is one force applied at the beginning on the trajectory, after which the only interference is from gravity.
    • If you were to draw a straight vertical line from the maximum height of the trajectory, it would mirror itself along this line.
    • The maximum height of a object in a projectile trajectory occurs when the vertical component of velocity, $v_y$, equals zero.

  • Defining Kinematics

    • To describe motion, kinematics studies the trajectories of points, lines and other geometric objects, as well as their differential properties (such as velocity and acceleration).
    • The study of kinematics can be abstracted into purely mathematical expressions, which can be used to calculate various aspects of motion such as velocity, acceleration, displacement, time, and trajectory.
    • Kinematic equations can be used to calculate the trajectory of particles or objects.

  • Basic Equations and Parabolic Path

    • Projectile motion is a form of motion where an object moves in parabolic path; the path that the object follows is called its trajectory.
    • The path that the object follows is called its trajectory.
    • Projectile motion only occurs when there is one force applied at the beginning on the trajectory, after which the only interference is from gravity.
    • Assess the effect of angle and velocity on the trajectory of the projectile; derive maximum height using displacement

  • Calculus with Parametric Curves

    • A common example occurs in physics, where it is necessary to follow the trajectory of a moving object.
    • A trajectory is a useful place to use parametric equations because it relates the horizontal and vertical distance to the time.

  • Zero Launch Angle

    • The path followed by the object is called its trajectory.
    • Projectile motion occurs when a force is applied at the beginning of the trajectory for the launch (after this the projectile is subject only to the gravity).
    • One of the key components of the projectile motion, and the trajectory it follows, is the initial launch angle.

  • Addition to Carbonyl Double Bonds

    • This explains the favored bonding alignment, known as the Bürgi-Dunitz trajectory.

  • The Physics of Bremsstrahlung

    • If we ignore the effect of radiation reaction of the trajectory of the charged particle, we can solve for its path exactly (at least in the classical limit) and then use the formulae for the radiation field that we derived a few weeks back.
    • We will approximate the exact trajectories shown in the left-hand panel of Fig.~1 by a simple straight line trajectory in which the acceleration of the particle lies mainly normal to the direction of the particle's motion.
    • First is to estimate at what impact parameter does the trajectory strongly differ from a straight line, so $\Delta v \sim v$, we get
    • The left panel gives the exact trajectory excluding radiation reaction, and the right panel shows how we will approximate the trajectory

  • Applications of Hyperbolas

    • This can be applied to a particle of any size, as long as gravity is the only force causing the orbital trajectory.
    • A parabolic trajectory does have the particle escaping the system.
    • If there is any additional energy on top of the minimum (zero) value, the trajectory will become hyperbolic, and so E is positive in the hyperbolic orbit case.
    • Blue is a hyperbolic trajectory (e > 1).
    • Green is a parabolic trajectory (e = 1).