Examples of trajectory in the following topics:
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- 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
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- 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.
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- In this model we consider a particle as being a point of mass which describes a trajectory in space which is modeled by a function giving its coordinates in space as a function of time.
- The potential field is given by a function $V:R^3 \rightarrow R$ and the trajectory is a solution of a differential equation.
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- A common example occurs in kinematics, where the trajectory of a point is usually represented by a parametric equation with time as the parameter.
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- Instantaneous velocity is always tangential to trajectory.