Time–frequency analysis: Difference between revisions

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[[Image:Distancedisplacement.svg|thumb|336px|Displacement versus distance traveled along a path.]]
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A '''displacement''' is the shortest [[distance]] from the initial to the final [[position (vector)|position]] of a point P.<ref>{{cite web
|url=http://www.physicsclassroom.com/Class/1DKin/U1L1c.cfm
|title=Describing Motion with Words
|author= Tom Henderson
|work= The Physics Classroom
|accessdate=2 January 2012}}
</ref>
Thus, it is the length of an imaginary straight path, typically distinct from the path actually travelled by P. A 'displacement vector' represents the length and direction of that imaginary straight path.


A [[position vector]] expresses the position of a point P in space in terms of a displacement from an arbitrary reference point O (typically the origin of a coordinate system). Namely, it indicates both the distance and direction of an imaginary motion along a straight line from the reference position to the actual position of the point.  
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A displacement may be also described as a 'relative position': the final position of a point ('''''R<sub>f</sub>''''') relative to its initial position ('''''R<sub>i</sub>'''''), and a displacement vector can be mathematically defined as the [[vector subtraction|difference]] between the final and initial position vectors:
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:<math>
  <li>[http://forum.joshsisto.com/profile.php?id=60835 http://forum.joshsisto.com/profile.php?id=60835]</li>
\boldsymbol{s}=\boldsymbol{R_f-R_i}=\Delta\boldsymbol{R}
 
</math>
  <li>[http://281091.free.fr/index.php?site=forum_topic&topic=4663 http://281091.free.fr/index.php?site=forum_topic&topic=4663]</li>
 
 
In considering motions of objects over time the instantaneous [[velocity]] of the object is the rate of change of the displacement as a function of time. The velocity then is distinct from the instantaneous [[speed]] which is the time rate of change of the distance traveled along a specific path. The velocity may be equivalently defined as the time rate of change of the position vector. If one considers a moving initial position, or equivalenty a moving origin (e.g. an initial position or origin which is fixed to a train wagon, which in turn moves with respect to its rail track), the velocity of P (e.g. a point representing the position of a passenger walking on the train) may be referred to as a relative velocity, as opposed to an absolute velocity, which is computed with respect to a point which is considered to be 'fixed in space' (such as, for instance, a point fixed on the floor of the train station).
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For motion over a given interval of time, the displacement divided by the length of the time interval defines the average velocity. (Note that the average [[velocity]], as a vector, differs from the [[average speed]] that is the ratio of the path length&#8202;—&#8202;a scalar&#8202;—&#8202;and the time interval.)
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== Rigid body ==
In dealing with the motion of a [[rigid body]], the term ''displacement'' may also include the [[rotation]]s of the body. In this case, the displacement of a particle of the body is called '''linear displacement''' (displacement along a line), while the rotation of the body is called '''[[angular displacement]]'''.
 
== Derivatives ==
For a position vector '''''s''''' that is a function of time ''t'', the derivatives can be computed with respect to ''t''. These derivatives have common utility in the study of [[kinematics]], [[control theory]], and other sciences and engineering disciplines.
    
    
[[Velocity]]
</ul>
:<math>\boldsymbol{v}=\frac{\text{d}\boldsymbol{s}}{\text{d}t}</math> (where d'''''s''''' is an [[Differential (infinitesimal)|infinitesimally]] small displacement)
 
[[Acceleration]]
:<math>\boldsymbol{a}=\frac{\text{d}\boldsymbol{v}}{\text{d}t}=\frac{\text{d}^2\boldsymbol{s}}{\text{d}t^2}</math>
 
[[Jerk (physics)|Jerk]]
:<math>\boldsymbol{j}=\frac{\text{d}\boldsymbol{a}}{\text{d}t}=\frac{\text{d}^2\boldsymbol{v}}{\text{d}t^2}=\frac{\text{d}^3\boldsymbol{s}}{\text{d}t^3}</math>
 
These common names correspond to terminology used in basic kinematics.<ref name='stewart'>{{cite book
|last= Stewart
|first= James
|authorlink=James Stewart (mathematician)
|title= [[Calculus]]
|publisher= Brooks/Cole
|year= 2001
|edition= 2nd
|isbn= 0-534-37718-1
|chapter= §2.8 - The Derivative As A Function
}}
</ref>  By extension, the higher order derivatives can be computed in a similar fashion.  Study of these higher order derivatives can improve approximations of the original displacement function.  Such higher-order terms are required in order to accurately represent the displacement function as [[Taylor series|a sum of an infinite series]], enabling several analytical techniques in engineering and physics.
 
==See also==
* [[Position vector]]
* [[Affine space]]
 
==References==
{{reflist}}
 
{{Kinematics}}
 
[[Category:Motion]]
[[Category:Length]]
 
[[Category:Vectors]]

Latest revision as of 02:46, 9 November 2014

Hollister Australia he says

So while it very cool that the artist that has foundfinancialsuccess with the chart topping Gnarls Barkley, could put out music that challenges, it also a sad reminder of whatintellectual property is treated like; Hollister Australia a commodity. "_A special edition book of Lynch's visuals for the album has been released and it is available here.

We are inside a catch 22, where many health professionals feel they cannot recommend Tai-chi because too much of Nike Free 3.0 the preliminary research is anecdotal. However, when Tai Chi is jockeying for position to get a crumb of the .5% of total NIH money going to ALL complimentary and alternative medical therapies .

3) The court system: The whole can do anything a man can do, empowered thing reminds me of a Nike Air Max 90 tactic John Stewart likes to use. He makes serious commentary that he wants to affect how people think, but when he gets called onto it, he says, I just a comedian.

The reality of the matter is that Councils can't solve this issue on their own. This is something we can and should do for ourselves.. In case your site is down or takes to long to open up when visitors are looking to get in, it may lead them to click out of your site and move on to the next. They will also more than likely not visit later on since they will remember their bad experience.

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NOTES: Only Sacramento and Washington have fewer wins on the road than Philly. Wilkins finished with 13 points. Pekovic stayed in Minnesota for the AllStar break rather than seek out the sun's rays and the sand as so many of his teammates did. He went ice fishing on a nearby lake, and Collins increased to him before the game and playfully asked him why he wasn't invited.

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