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There is very little change in the trajectory over the time it takes for the oscillation to damp out. Generally this oscillation is high frequency (hence short period) and is damped over a period of a few seconds. A real-world example would involve a pilot selecting a new climb attitude, for example 5° nose up from the original attitude.
Other frames can be defined on those mobile objects to deal with relative positions for other objects. Finally, attitudes or orientations can be described by a relationship between the external frame and the one defined over the mobile object. The orientation of a vehicle is normally referred to as attitude.
Since the velocity of the object is the derivative of the position graph, the area under the line in the velocity vs. time graph is the displacement of the object. (Velocity is on the y-axis and time on the x-axis. Multiplying the velocity by the time, the time cancels out, and only displacement remains.)
The attitude indicator (AI), also known as the gyro horizon or artificial horizon, is a flight instrument that informs the pilot of the aircraft orientation relative to Earth's horizon, and gives an immediate indication of the smallest orientation change. The miniature aircraft and horizon bar mimic the relationship of the aircraft relative to ...
The trajectory of a particle is a vector function of time, (), which defines the curve traced by the moving particle, given by = ^ + ^ + ^, where (), (), and () describe each coordinate of the particle's position as a function of time.
In geometry, the orientation, attitude, bearing, direction, or angular position of an object – such as a line, plane or rigid body – is part of the description of how it is placed in the space it occupies. [1] More specifically, it refers to the imaginary rotation that is needed to move the object from a reference placement to its current ...
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Mathematically, the duality between position and momentum is an example of Pontryagin duality. In particular, if a function is given in position space, f(r), then its Fourier transform obtains the function in momentum space, φ(p). Conversely, the inverse Fourier transform of a momentum space function is a position space function.