Talk:Kinematics - Knowledge

1336:

biomechanics, are all sciences in which kinematics is applied to study celestial bodies, mechanical systems, multi-link biological systems. But first of all, we need to explain how (linear) kinematics describes the motion of a point. We need to assume that the reader knows nothing about kinematics. What would you say if a biomechanist inserted in the introduction a picture about the kinematics of a twisting somersault? For a biomechanist, that would be much more attractive than the steam engine. And what about rotation, revolution, precession and nutation of Earth? These are fascinating examples, however they are complex, and our readers are neither advanced students, nor mechanical engineers, nor biomechanists. They need much simpler examples. I know that this may be boring for expert editors like you (according to Hawking, Albert Einstein was offered positions in many Universities, but he chose a "research position with the Prussian Academy of Sciences in Berlin because it freed him from teaching duties"), but our main purpose is not having fun. We are here to be of service for our readers, and most of them are beginners.

1306:

of the study of kinematics. I believe he is well-meaning and would like to see something more mathematical in appearance, but prefers a blank page until someone else finds something to his liking. This means that he does not see (i) the straight line movement in the expansion cylinder guided by Watt's straight-line linkage, (ii) the four-bar linkage formed by the walking beam input crank and its coupler that drives the output crank rotating the main drive pulley, and (iii) the fly-ball governor which is rotating slider crank that provides feedback control of the power source. These are all fundamental kinematic elements assembled into arguably one of the most important technological developments in history, the Boulton-Watt steam engine. It is probably fair to say that the ability to generate mechanical forces and movement with a steam engine also drove the study of mechanics, in general, and kinematics, in particular.

369: 1517: 2411:

integration graphical representation and derivation is awkward and unnecessarily weedy. The graph is lacking significant annotations and those that are there are unhelpful. (If I had to, I would have used the area of a trapezoid formula instead of calculating areas of a rectangle and triangle and then adding them together.) The text here uses a lot of unintelligible and incorrect terminology. The graph caption is a good example. Figure 2 is out of place here having undefined terms and parameters involving non-inertial reference frames yet to be addressed.

1381:"Needless to say, I disagree"? Are you assuming that everybody should agree with you? Discussions imply the need to interact. On Knowledge, consensus is needed to take decisions. I will expand on just one of the points you ignored in your reply: the article is not about objects which move. Showing an object which can move (or even an animation of a moving object) is not enough to illustrate kinematics. The picture should at least show a trajectory, possibly an "arrow" representing a kinematic quantity. In other words, something that "describes" the motion. 1469: 471: 443: 1298: 264: 254: 233: 200: 1366:

rotation, revolution, precession and nutation of the earth. But, I see that even these are considered too complex for our readers and not helpful for beginners. Again, I disagree. Finally, among the very first problems in physics are the kinematics of particles moving along a straight line and moving on a circle. In my opinion, even beginners would recognize that the components of a steam engine contain many particles that are moving along straight lines and on various circles.

359: 338: 1098:

sections after "Integral relations" soon. The rest of it needs much standardization. "Linear Motion" shouldn't be the primary heading. It should be "Particle Kinematics" and "Linear Motion" Should appear as a sub-category in Particle Kinematics. Further, the average quantities were introduced after the instantaneous ones. Scanty remarks were made for the limiting definition of velocity or acceleration.

531: 2432: 457: 1550:

knows that kinematics is a branch of physics, not a branch of mechanical engineering. Kinematics was first used by Galileo and Newton to describe the motion of projectiles, sliding objects, balls rolling along inclined planes, penduli, and celestial bodies. As far as I know, most physicists do not describe the motion of machines when they explain kinematics in undergraduate courses.

1624:

the introduction", "Watt's steam engine", "Wheel", and "Four-bar linkage") showed no point of view and objectively described the contents of the following text, respecting the "historical nature" of the discussion. See also my note above, where I explained everything. This kind of mild refactoring can significantly improve the readability of the page, and this, according to

191: 704:

jounce is not referenced (though it is linked). The notation of the graphic was unexplained -- What is x? What is f(x)? What does the "prime" notation mean? r, dr/dt, d^2r/dt^2, etc would be more appropriate. Wouldn't these be better represented by a table? Is an article on kinematics even the appropriate place for this? --

1322:

example in the introduction of an article about kinematics. Moreover, that picture was not even about the kinematics of an engine, but showed only its structure (the motion of the engine is not described at all; no kinematic quantity is mentioned or represented). The picture belongs in the introductions of articles such as

2219: 2410:

Remainder of section from "We also know that..." repeats the earlier derivation, is circuitous, and poorly annotated. If there is no WP page that diagrams the time differentials of position, velocity, and acceleration and explains their relations anywhere else, it could be useful here. The velocity

1604:

I believe it is inappropriate to reformat talk pages, particular entries by other editors. This removes the historical nature of an evolving conversation. By taking this action Paolo.dL has reached beyond his assumption of final authority regarding my choice of figure, to domination of my responses

1431:

regarding this topic" (which is true). I remember what I felt whenever somebody reverted some edits of mine without my approval, in articles that I highly contributed to improve, sometimes even without offering adeguate edit summaries. So, I understand your passion, but still you need to abide to the

918:

This article seems a collage of statements taken from different chapters of a physics book, and assembled whithout a logical order, and without specifying clearly where they belong in. There are various levels of kinematics, and either they should be treated separately, starting from the simplest, or

1491:

Yet another figure showing a machine. Nothing in it helps the reader to understand what kinematic is (there is a vector Q which is not described, whose meaning is quite difficult to understand even for me; it may possibly be meant to describe an angular kinematic quantity such as angular velocity or

1365:

Needless to say, I disagree with most of our colleague's statements. I hope I was clear in the discussion above that the steam engine is an excellent portrayal of kinematics. I can also say that I would very much appreciate a picture about the kinematics of a twisting somersault, and one about the

1305:

I have to say that Paolo.dl's edits to this article are welcome. Unfortunately, he puts his long explanations into the edit description, which is interesting reading but makes it difficult to respond. He deleted the picture of the steam engine even though almost every feature illustrates an aspect

1174:

I concluded that I could not fix the section on particle kinematics without deleting large portions, which did not seem inappropriate. So instead, I have appended a section on the position, velocity and acceleration of points in a moving rigid body. It is a rather detailed derivation that seems to

798:

Mathematics professionals seem to overlook the practical issues regarding brevity. At a time when publishing was expensive the writers and teachers needed to keep their work as brief as possible. Now with digitisation the primary hindrances have been overcome. Fed on a diet of barley some forget the

662:

in the equations, while the relationship between the velocities is vital in understanding the equations. Additionally, if initial and final angular displacements are used in describing angular kinematics, it seems reasonable to be consistent and use initial and final linear displacement to describe

1623:

is allowed in Knowledge. Especially if it is mild and respectfully performed as in this case. I only changed two section titles, which referred directly and inappropriately to me rather than to the real topic of the discussion, and added two other subsection titles. All the new titles ("Picture for

1527:

Well, it seems I am in the position of trying to find a figure that satisfies the personal tastes of our colleague Paolo.dL. As far as I can tell he does not want illustrations of the moving parts of a complex machine like the Boulton and Watt steam engine, nor does he want the simplest example of

1194:

I think the section on particle kinematics appears to be general discussion of elementary physics. It discusses reference frames, the definition of the derivative, integration of ballistic trajectories, relative position vectors, and more. I will leave it alone, because I just cannot quite figure

1138:

This article focusses on particle kinematics which is essentially the differential geometry of a curves. I would like to stream-line this presentation of particle kinematics somewhat, and then expand it to the kinematics of rigid bodies. Things get more interesting when we consider the kinematics

1574:

As, I wrote above, kinematics was first used to describe the motion of projectiles, sliding objects, balls rolling along inclined planes, penduli, and celestial bodies. A description of Galileo's experiments with sliding blocks or rolling balls, for instance, is perfect to introduce the concept of

1321:

Please, do not try to guess what I can see or not see in the picture of the steam engine (especially if you assume that I can't see). I greatly appreciate most of your edits, so I value your opinion, but I removed the picture because I believe that the kinematics of an engine is not an appropriate

1076:

object can be divided into a caus and an effect. fact is that one has to blend out the affected object and blends out the cause while watching the affected object. it´s just a game of zooming in and out and arbitrarily either blending out the surroundings or the details as if they would disappear.

1097:

Have changed the initial sections today. The exposition wasn't smooth. There was no mention of the idea of rest and motion stemming out from the fundamental frame dependence of position vectors. Come to think of it, there was no mention of reference frames at all. Have added that. Will get to the

703:

I removed the "First to Fourth Derivatives of Position" graphic. It was an image with four equations: f(x) = position, f′(x) = velocity, f′′(x) = acceleration, f′′′(x) = jerk, and f′′′′(x) = jounce. The term jerk is referenced in the text but not in the section containing the graphic. The term

1549:

About this new figure that McCarthy proposes, it is very similar to the previous ones. Also, it seems he confuses kinematics with kinematics of machines. His sentence "the four-bar linkage illustration is the focus of most courses on Kinematics" reveals his bias, although I am sure he perfectly

1075:

in the first one the authors leave out that the motion of objects appears over time. also a problem is that it´s arbitrary what a cause is, because one can see the "cause" as a part of the system and this system has been caused by some other causes. one could also zoom in and say that the moving

2089: 2397:

Strike "In the case of acceleration..." Replace with "For the case of linear motion, the difference of positions vector, velocity vectors, and acceleration vectors will be colinear. All angles between vectors will be 0° or 180° giving 1 or -1 for the cosine of these angles respectively. The

1210:

Let me just add that the first sentence "Particle kinematics is the study of the kinematics of a single particle." captures the redundancy that is present in much of this section. Having said this, it is not correct that there is nothing that is useful. It is just difficult to sort it out.

1049:

Most of the symbols here are quite ccomplex. In my first year at university studying Mech. Eng. this was even more complicated as you had to learn what each symbol stood for. Instead of writing down the equations can we have a table to the side telling us what each symbol means and how it is

1335:

In physics textbooks, kinematics is first described for the motion of a point, then for rigid bodies, and sometimes also for multi-body systems. The motion of a mechanical system, therefore, represents one of the most complex possible examples of motion. Astronomy, mechanical engineering,

1682:

I am sorry for the long chain of revisions. I just wanted to adjust the order of topics so that it proceeded from particle kinematics to planar rigid body kinematics and then to spatial rigid body kinematics, but the notation and concepts needed sorting out much more than I expected.

1750:

I am sorry that I have made a long list of revisions without explanation. I thought I could do this easily and quickly, but it did not go as smoothly as I had hoped. I have provided the matrix calculations that define angular velocity and angular acceleration for a rotating body.

1553:

McCarthy has been totally ignoring most of my comments, and this unfortunately prevents a constructive discussion between us. Possibly, he thinks exactly the same thing about me. This is why I insist that we need the opinion of other editors, and keep asking him to be patient.

1528:

rotating disk which he considers to be a machine. He does want arrows and some mathematical display of movement. I am fairly certain, therefore, that he will not accept the four-bar linkage illustration, though it is the focus of most courses on Kinematics. I am at a loss.

2444: 1581:, where space, time, and time-variant values of velocity and acceleration are shown. (Remember to press the start button; if you can't see the animation, probably you need to install Java runtime environment). By the way, a sliding plane is considered to be a 1982: 799:

taste of a multi-layered chocolate pastry overflowing with cream and icing :-) ;-) . I don't need to quote Pages 2-3, art. 0.1 Possible uses of history..., I. Grattan-Guinness, titled, From the Calculus to Set Theory, Princeton University Press.

557:

Removed the section on motion under gravity; it was poorly written, did not fit in with the rest of the article, and wrong. It seemed to say that Gallileo said that objects of different masses fall at different rates, which is clearly incorrect.

990:

Please do not use the symbol s for a position vector but only the symbol r. s is used in mathmatics and physics for 's = the distance along some curve C in space as measured from some fixed point' (cited from Standard Mathematical Tables). And

2095: 1632:

of WP:Refactor, about "Changing section titles". Johnuniq wrote: "I did one such change recently because the article talk page section heading was addressed to a specific editor, and it is usually best to avoid unnecessary confrontation".

1341:

Last but not least, the kinematics of mechanical systems is not described in this article (and this is consistent with most introductory physics texbooks, which focus mainly on the kinematics of particles and rigid bodies). According to

1158:

After revising the lead and adding section on rigid transformations, I am now examining the section on particle kinematics. This section seems to be repeating basic results of vector calculus. I am not sure I can salvage much of it.

723:

While a purely mathematical treatment is nice, we should consider some plain language description of what each term does. We also need the history of kinematics, it's major developers, and the problems they were interested in solving.

1346:, the introduction of an article should only summarize the article's main topics. The picture about the steam engine is not appropriate for any of the sections of the article, and therefore not appropriate for its introduction. 1988: 1435:

In this case, accoding to good sense, politeness, respect for each other and Knowledge policies, we need to wait for contributions by other editors, and in the meantime we need to accept the situation as it was before

621:

to the Fundamental Equations heading. Give me your thoughts - I like that notation a bit better, it's more common, and a bit easier to understand. It may not reconcile with the vector notation used, but it is algebra.

1496:, and its position in the picture is quite unusual for a such a vector). Please do not insert new figures in the introduction of the article. Please patiently wait for the opinion of other editors in this talk page. 2384:

This section is unfocussed, lacks formal vector algebra to match earlier sections, and poorly explained equation derivation for constant acceleration (can be shown from time dependent acceleration in few steps).

153: 1399:

I believe we have established that there is no consensus regarding your criteria for acceptable figures for this article. Therefore, please replace it until you can find another editor who agrees with you.

1901: 2521: 999:

ds)'(same source) It is extremely confusing to use s for a position vector. In it's whole this is a confusing text, mixing different elements together with not so clear relationships with each other.

2479: 823:

Can anyone direct me to an article on relativistic kinematics (if one exists)? If there's no such article yet, it should probably be created either separately or as a subsection of kinematics.

320: 1605:

to his actions. This behavior should be banned on Knowledge. The fact that nothing will happen should put to rest the myth that there is another editor who will regulate his actions.

851:

Where do you see d being used for the difference? Δ is used for difference in the section "Algebraic equations." Elsewhere d is used only for the differential, as far as I can see.

892:

The above comment is true however it must be added that u was formerly used for denoting initial velocity. The same applies the acceleration which can be denoted by either f or by a

607:

This page contains several statements at the end about angular "position" and angular velocity that are non-general; that is, they only apply to a two dimensional or planar problem.

2511: 572:+++ The material is copy-written by a textbook manufacture, nearly word for word. This article needs to be deleted and rewritten with out infringing on the published works+++++. 2526: 2551: 2394:

At 1st citation needed: Strike . Replace phrase with "By definition of the dot product" before equation. There is no need to cite a fundamental vector algebra definition.

1831: 632:

I notice that the change in the algebraic equations for linear kinematics are not notated consistently with the angular portion. I prefer describing linear kinematics using

2214:{\displaystyle (\mathbf {P} -\mathbf {P} _{0})\circ \mathbf {A} =\left(\mathbf {V} -\mathbf {V} _{0}\right)\circ \left({\frac {\mathbf {V} +\mathbf {V} _{0}}{2}}\right)\ ,} 1907: 204: 942:

Angular kinematics in 2-D and 3-D (for instance, in 3-D, the angular position of a particle rotating about a point cannot be described by a simple angle; you need a

147: 1629: 2304: 2300: 2286: 1851: 682:

Physics is a beautiful subject which is not confusing in the least. Now as for this article it seems to be a crash course in kinematics and for that it is fine.

926:

In this context it is not correct, in my opinion, to use the expression "translational kinematics"; the word "translational" is used only for rigid body motion.

425: 598:

This article contains lots of nonstandard notation. This is potentially confusing. More standard notation can be found in numerous physics texts including:

2566: 1273:

I have commented out a few sections because they were non-standard, duplicative or irrelevant. I think this helps the remaining material flow much better.

789:. I have skimmed through the book but didn't find any history about equations of motion. Everywhere in wikipedia, most articles of mathematics lack history. 2536: 310: 2561: 860:

I agree, I have only found d to be used for the differential, which is its standard usage and is not the same as the difference described by delta. See

511: 79: 2084:{\displaystyle \left(\mathbf {P} -\mathbf {P} _{0}\right)\circ \mathbf {A} =\left({\frac {\mathbf {V} +\mathbf {V} _{0}}{2}}\right)\circ \mathbf {A} t} 2506: 521: 2546: 839:

In this article, it seems the notation is 'd' for difference. Whilst this makes sense, to people who have learnt it with the delta it is confusing.

663:

linear kinematics instead of using Δ. I believe it may be sufficient to simply notate the linear equations in both ways, which is what I have done.

415: 1235:

can be revised so the formulas for a moving particle are easier to understand. I will work on this on my user page and drop it in for evaluation.

2516: 1444:

edits). This means that the introduction should stay without a figure, because the figure I removed was added by you on the 29th of December with

2571: 1718: 1254:

This section seems to be a duplicate of the position, velocity and acceleration in cylindrical coordinates. I will add it as a special case.

966:

Linear kinematics in 2-D and 3-D, which describes translation (it is the same as above, but first you need to select a point fixed on the body)

837:

I have long understood in Physics and Maths that difference (e.g. the difference between two speeds) is notated with a Greek 'Delta' Δ symbol.

755:

also gives an overview of what happened from 1600 to 1876. I've linked all the persons mentioned to Knowledge, and even wrote an article about

286: 969:

Angular kinematics in 2-D and 3-D, which describes the rotation (and this is a complex part, with several different conventions, explained in

368: 2531: 899: 689: 85: 2452: 579: 752: 1702:

In the section "Velocity and speed" the symbol 's' (distance travelled) is used a few times, but it has never been introduced/defined.

1000: 559: 487: 2483: 2556: 1079: 391: 44: 2541: 2282:

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

277: 238: 1019:

It appears that links 1.3.1 to 1.3.4 are broken, that is, they don't move you to their corresponding subsections when clicked...

2404:

Strike following sentence. Define scalar variables after next equation, "where v = |V|, a = |A|, and ∆x = |P| - |P0| = x - x0."

1620: 1432:

policies on Knowledge: no editor can impose his own criteria, not even one who completely wrote an ecellent article from scratch.

1858: 1780:, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section. 2501: 99: 30: 478: 448: 104: 20: 1791: 1472:

Figure from Kinematics of Machinery 1876: A wheel, constructed of perfectly rigid material, supported between two mounts.

1415:

Your reply appears so naively biased to me that I feel empahtetic, rather than offended. You should either have written: "

382: 343: 74: 168: 2347: 2237: 1034: 213: 135: 65: 1714: 1103: 2416: 2303:

to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the

1195:

it out. Instead, I propose to work on the section on kinematic constraints, which is important and neglected.

2464: 2272: 1384:

Since you totally rejected my points, I suggest to wait for contributions by other editors to this discussion.

903: 743: 693: 623: 583: 1004: 2448: 2358:

Copying section on "Kinematics of a particle trajectory in a non-rotating frame of reference" to Wikiversity

2338: 2264: 1756: 1735: 1688: 1610: 1533: 1481: 1468: 1405: 1371: 1311: 1278: 1259: 1240: 1216: 1200: 1180: 1164: 1148: 1083: 563: 129: 109: 2412: 1124: 1099: 1055: 1069:

cinematics: "describes the motion of objects without consideration of the causes leading to the motion."

2370: 2322:

If you have discovered URLs which were erroneously considered dead by the bot, you can report them with

2310: 1710: 1516: 806: 219: 2263:. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit 756: 470: 442: 263: 125: 2233: 1977:{\displaystyle \mathbf {P} -\mathbf {P} _{0}=\left({\frac {\mathbf {V} +\mathbf {V} _{0}}{2}}\right)t} 1030: 2225: 1706: 1668: 1022: 895: 685: 575: 872: 674: 190: 2460: 2366: 1297: 970: 786: 782: 664: 161: 55: 1811: 1127: 486:

on Knowledge. If you would like to participate, please visit the project page, where you can join

390:

on Knowledge. If you would like to participate, please visit the project page, where you can join

285:

on Knowledge. If you would like to participate, please visit the project page, where you can join

175: 2435:

This article was the subject of a Wiki Education Foundation-supported course assignment, between

2229: 1752: 1731: 1684: 1638: 1625: 1606: 1590: 1559: 1529: 1501: 1477: 1453: 1401: 1389: 1367: 1355: 1307: 1274: 1255: 1236: 1212: 1196: 1176: 1160: 1144: 709: 608: 269: 70: 2307:

before doing mass systematic removals. This message is updated dynamically through the template

253: 232: 2323: 1327: 1120: 1051: 759:

who didn't have one. I guess Monge, Hachette and Lanz should be mentioned as pioneers here. --

51: 1175:

balance the elementary nature of the section on particle kinematics. Maybe this will work.

1140: 802: 2330: 1664: 1493: 2363: 141: 2289:, "External links modified" talk page sections are no longer generated or monitored by 1628:, is appropriate and in some cases desirable. See also the last comment by Johnuniq on 1582: 748: 374: 2329:

If you found an error with any archives or the URLs themselves, you can fix them with

1836: 1800:

Last edited at 18:22, 3 October 2006 (UTC). Substituted at 21:14, 29 April 2016 (UTC)

2495: 1777: 1634: 1586: 1555: 1497: 1449: 1385: 1351: 1343: 977: 764: 705: 456: 1804:

Invalid division by a vector in "Particle trajectories under constant acceleration"

1787: 1323: 730: 1585:, but the focus here is on the kinematics of the block (which is not a machine). 1409: 1375: 1315: 919:

the simpler levels should be defined as special cases or the most complex level.

2431: 2362:

I am copying this section over to a course on robotic mechanics on Wikiversity.

2296: 1476:

This figure has an arrow and comes from a book called Kinematics of Machinery.

1026: 943: 778: 727: 358: 337: 282: 2295:. No special action is required regarding these talk page notices, other than 2256: 1232: 954: 953:

Here, and only here, you define the concepts of translation and rotation (see

842: 618: 530: 364: 259: 24: 2273:

https://web.archive.org/web/20070601020244/http://www.physclips.unsw.edu.au/

1119:

can't begin an article with a quote. no can do. where should it be moved? –

1072:

dynamics: "customarily refers to the time evolution of physical processes."

1577: 1521: 852: 841:

Is this simply an Australian notation? Can we look into this some how? -

824: 760: 483: 871:

Why is u used to represent initial velocity? Is this standard notation?

387: 914:

The levels are not clearly defined and the terminology is questionable

2364:

https://en.wikiversity.org/Robotic_Mechanics_and_Modeling/Kinematics

2276: 1492:

angular acceleration, but its direction is not consistent with the

2487: 2468: 2420: 2374: 2352: 2241: 1760: 1739: 1722: 1692: 1672: 1642: 1614: 1594: 1563: 1537: 1515: 1505: 1485: 1467: 1457: 1393: 1359: 1296: 1282: 1263: 1244: 1220: 1204: 1184: 1168: 1152: 1107: 1087: 1059: 1038: 1008: 980: 907: 875: 855: 845: 827: 810: 768: 713: 697: 677: 667: 626: 611: 587: 567: 2388:

V(t) integration assumes constant acceleration without mention.

1423:

criteria" (which would have revealed more openly your bias) or "

734: 184: 15: 2426:

Wiki Education assignment: PHY 381 History of Modern Physics

538:

This article has been marked as needing immediate attention.

529: 1896:{\displaystyle \mathbf {A} t=\mathbf {V} -\mathbf {V} _{0}} 889:

are the standard methods of representing initial velocity.

2267:

for additional information. I made the following changes:

1575:

kinematics. For instance, see this intuitively appealing

2260: 1772: 1445: 1419:

have established that there is no consensus regarding

160: 2522:

Knowledge level-4 vital articles in Physical sciences

2098: 1991: 1910: 1861: 1839: 1814: 1746:

Revisions to section on the rotation of a rigid body

1427:

have established that there is no consensus between

601:

Halliday&Resnick, Johnson&Cutnell, Serway

482:, a collaborative effort to improve the coverage of 386:, a collaborative effort to improve the coverage of 281:, a collaborative effort to improve the coverage of 2398:vectors can be written as their scalar magnitudes: 2299:using the archive tool instructions below. Editors 2213: 2083: 1976: 1895: 1845: 1825: 1570:Ball rolling or block sliding along inclined plane 923:Level 1: Point (or point mass, or particle) motion 781:I have also written the same about history in the 654:because there is no obvious relationship between 33:for general discussion of the article's subject. 1776:, and are posted here for posterity. Following 2285:This message was posted before February 2018. 2512:Knowledge vital articles in Physical sciences 1770:The comment(s) below were originally left at 1113: 174: 8: 2475:All Rights Reserved®️ +TheKIN3TEKInitiative. 2527:B-Class vital articles in Physical sciences 2552:B-Class physics articles of Top-importance 2401:v^2 = v0^2 + 2•a•(x - x0) = v0^2 + 2•a•∆x 2255:I have just modified one external link on 2223: 1808:The substitution should take into account 1301:The Boulton & Watt Steam Engine, 1784. 437: 332: 227: 2190: 2185: 2176: 2173: 2155: 2150: 2141: 2128: 2116: 2111: 2102: 2097: 2073: 2054: 2049: 2040: 2037: 2025: 2011: 2006: 1997: 1990: 1955: 1950: 1941: 1938: 1925: 1920: 1911: 1909: 1887: 1882: 1873: 1862: 1860: 1838: 1815: 1813: 751:. The book is history in itself, but its 1730:I will make this correction. Thank you 1520:Illustration of a four-bar linkage from 2480:2406:5A00:1007:6300:C99D:127E:6997:5E98 1143:. I will try to make that connection. 439: 334: 229: 188: 673:Of course its confusing, its Physics! 1660:Add notes for any further work needed 7: 1011:(I am Huibc in the Dutch Knowledge) 476:This article is within the scope of 380:This article is within the scope of 275:This article is within the scope of 2567:Robotics articles needing attention 1114:can't begin an article with a quote 218:It is of interest to the following 23:for discussing improvements to the 2537:High-priority mathematics articles 2440: 2436: 1139:of articulated systems such as in 995:= the vector element of a curve (= 14: 2562:High-importance Robotics articles 2407:'Curvelinear', not 'curvaceous.' 2391:'translation' not 'displacement' 2277:http://www.physclips.unsw.edu.au/ 2259:. Please take a moment to review 1778:several discussions in past years 946:or an angular position vector...) 295:Knowledge:WikiProject Mathematics 2507:Knowledge level-4 vital articles 2443:. Further details are available 2430: 2186: 2177: 2151: 2142: 2129: 2112: 2103: 2074: 2050: 2041: 2026: 2007: 1998: 1951: 1942: 1921: 1912: 1883: 1874: 1863: 1816: 939:Linear kinematics in 2-D and 3-D 741:On Wikisource, you can now find 469: 455: 441: 367: 357: 336: 298:Template:WikiProject Mathematics 262: 252: 231: 198: 189: 45:Click here to start a new topic. 2547:Top-importance physics articles 1250:Point object in circular motion 516:This article has been rated as 420:This article has been rated as 315:This article has been rated as 2517:B-Class level-4 vital articles 2380:Relative Acceleration problems 2242:13:52, 24 September 2016 (UTC) 2122: 2099: 1190:Particle kinematics needs work 496:Knowledge:WikiProject Robotics 1: 2572:WikiProject Robotics articles 2459:— Assignment last updated by 1826:{\displaystyle \mathbf {A} t} 1673:11:27, 28 February 2012 (UTC) 1522:Kinematics of Machinery, 1876 1283:23:28, 31 December 2011 (UTC) 1264:22:50, 31 December 2011 (UTC) 1245:21:46, 31 December 2011 (UTC) 1233:Kinematics#Coordinate systems 1221:07:39, 31 December 2011 (UTC) 1205:07:33, 31 December 2011 (UTC) 1185:04:44, 31 December 2011 (UTC) 1169:07:19, 30 December 2011 (UTC) 1153:13:11, 25 December 2011 (UTC) 1128:10:46, 28 February 2011 (UTC) 1108:19:27, 18 November 2009 (UTC) 1088:14:25, 2 September 2009 (UTC) 1009:16:54, 29 November 2007 (UTC) 856:16:23, 18 February 2007 (UTC) 846:05:24, 18 February 2007 (UTC) 777:Better late than never! Like 627:08:10, 6 September 2006 (UTC) 588:22:49, 23 February 2010 (UTC) 499:Template:WikiProject Robotics 490:and see a list of open tasks. 400:Knowledge:WikiProject Physics 394:and see a list of open tasks. 289:and see a list of open tasks. 42:Put new text under old text. 2532:B-Class mathematics articles 2469:02:52, 26 January 2023 (UTC) 2375:20:13, 20 January 2020 (UTC) 1292: 1288:Picture for the introduction 828:03:09, 5 November 2006 (UTC) 403:Template:WikiProject Physics 2421:02:15, 31 August 2020 (UTC) 1643:00:30, 7 January 2012 (UTC) 1615:22:54, 6 January 2012 (UTC) 1595:21:11, 6 January 2012 (UTC) 1564:20:30, 6 January 2012 (UTC) 1538:16:59, 6 January 2012 (UTC) 1506:10:21, 6 January 2012 (UTC) 1486:00:28, 6 January 2012 (UTC) 1458:16:52, 5 January 2012 (UTC) 1410:15:20, 5 January 2012 (UTC) 1394:12:32, 5 January 2012 (UTC) 1376:06:48, 5 January 2012 (UTC) 1360:18:07, 4 January 2012 (UTC) 1316:16:50, 4 January 2012 (UTC) 1060:22:14, 23 August 2009 (UTC) 1039:18:34, 25 August 2008 (UTC) 833:Specific notation confusion 811:10:45, 14 August 2015 (UTC) 769:12:27, 17 August 2010 (UTC) 744:The Kinematics of Machinery 612:09:20, 25 August 2006 (UTC) 50:New to Knowledge? Welcome! 2588: 2488:21:29, 3 August 2023 (UTC) 2316:(last update: 5 June 2024) 2252:Hello fellow Wikipedians, 1045:Symbols and their meanings 951:Level 2: Rigid body motion 908:12:05, 30 March 2008 (UTC) 698:12:02, 30 March 2008 (UTC) 668:20:59, 22 March 2007 (UTC) 568:14:33, 30 April 2008 (UTC) 522:project's importance scale 426:project's importance scale 2557:B-Class Robotics articles 1785: 1761:16:38, 13 July 2012 (UTC) 1740:04:58, 27 June 2012 (UTC) 1723:13:08, 26 June 2012 (UTC) 1693:10:03, 22 June 2012 (UTC) 1649:Robotics attention needed 981:22:06, 28 June 2007 (UTC) 537: 515: 464: 419: 352: 314: 247: 226: 80:Be welcoming to newcomers 2542:B-Class physics articles 1773:Talk:Kinematics/Comments 986:Position vector: r or s? 936:Linear kinematics in 1-D 876:02:14, 1 June 2007 (UTC) 819:Relativistic kinematics? 719:History and Explaination 714:22:34, 2 June 2010 (UTC) 678:20:56, 14 May 2007 (UTC) 321:project's priority scale 2353:04:53, 6 May 2017 (UTC) 2248:External links modified 1698:Symbol s not introduced 1600:Reformatting Talk Pages 1440:edits (not just before 1134:Revisions to Kinematics 1065:dynamics and cinematics 278:WikiProject Mathematics 2502:B-Class vital articles 2215: 2085: 1978: 1897: 1847: 1827: 1621:Refactoring talk pages 1524: 1473: 1302: 1269:Commented out sections 553:"motion under gravity" 534: 75:avoid personal attacks 2447:. Student editor(s): 2216: 2086: 1979: 1898: 1848: 1828: 1578:interactive animation 1519: 1471: 1300: 533: 205:level-4 vital article 100:Neutral point of view 2297:regular verification 2096: 1989: 1908: 1859: 1837: 1812: 1231:I think the section 624:Democritus the Minor 617:I added the section 479:WikiProject Robotics 301:mathematics articles 105:No original research 2287:After February 2018 1792:Physics WikiProject 1293:Watt's steam engine 971:rotation (geometry) 787:equations of motion 619:Algebraic equations 383:WikiProject Physics 2449:Jeffrey Sucuzhanay 2445:on the course page 2341:InternetArchiveBot 2292:InternetArchiveBot 2211: 2081: 1974: 1893: 1843: 1823: 1766:Assessment comment 1525: 1474: 1303: 1227:Coordinate systems 535: 270:Mathematics portal 214:content assessment 86:dispute resolution 47: 2317: 2244: 2228:comment added by 2207: 2200: 2064: 1965: 1846:{\displaystyle t} 1798: 1797: 1726: 1709:comment added by 1544: 1328:mechanical system 1041: 1025:comment added by 910: 898:comment added by 700: 688:comment added by 578:comment added by 550: 549: 546: 545: 542: 541: 502:Robotics articles 436: 435: 432: 431: 331: 330: 327: 326: 183: 182: 66:Assume good faith 43: 2579: 2471: 2453:article contribs 2442: 2441:24 December 2022 2438: 2437:7 September 2022 2434: 2413:EvolutionOfTruth 2351: 2342: 2315: 2314: 2293: 2220: 2218: 2217: 2212: 2206: 2205: 2201: 2196: 2195: 2194: 2189: 2180: 2174: 2165: 2161: 2160: 2159: 2154: 2145: 2132: 2121: 2120: 2115: 2106: 2090: 2088: 2087: 2082: 2077: 2069: 2065: 2060: 2059: 2058: 2053: 2044: 2038: 2029: 2021: 2017: 2016: 2015: 2010: 2001: 1983: 1981: 1980: 1975: 1970: 1966: 1961: 1960: 1959: 1954: 1945: 1939: 1930: 1929: 1924: 1915: 1902: 1900: 1899: 1894: 1892: 1891: 1886: 1877: 1866: 1852: 1850: 1849: 1844: 1833:instead of only 1832: 1830: 1829: 1824: 1819: 1783: 1782: 1775: 1725: 1711:Leen Droogendijk 1703: 1543: 1512:Four-bar linkage 1141:robot kinematics 1110:soumengoswami10 1020: 893: 683: 590: 504: 503: 500: 497: 494: 473: 466: 465: 460: 459: 458: 453: 445: 438: 408: 407: 406:physics articles 404: 401: 398: 377: 372: 371: 361: 354: 353: 348: 340: 333: 303: 302: 299: 296: 293: 272: 267: 266: 256: 249: 248: 243: 235: 228: 211: 202: 201: 194: 193: 185: 179: 178: 164: 95:Article policies 16: 2587: 2586: 2582: 2581: 2580: 2578: 2577: 2576: 2492: 2491: 2477: 2458: 2428: 2382: 2360: 2345: 2340: 2308: 2301:have permission 2291: 2265:this simple FaQ 2250: 2184: 2175: 2169: 2149: 2140: 2136: 2110: 2094: 2093: 2048: 2039: 2033: 2005: 1996: 1992: 1987: 1986: 1949: 1940: 1934: 1919: 1906: 1905: 1881: 1857: 1856: 1835: 1834: 1810: 1809: 1806: 1771: 1768: 1748: 1704: 1700: 1680: 1651: 1602: 1572: 1514: 1494:right hand rule 1466: 1295: 1290: 1271: 1252: 1229: 1192: 1136: 1116: 1100:Soumengoswami10 1095: 1067: 1047: 1017: 988: 916: 900:117.194.225.190 888: 884: 869: 835: 821: 757:José María Lanz 721: 690:117.194.225.190 645: 638: 596: 594:Sundry comments 573: 555: 518:High-importance 501: 498: 495: 492: 491: 454: 452:High‑importance 451: 405: 402: 399: 396: 395: 373: 366: 346: 300: 297: 294: 291: 290: 268: 261: 241: 212:on Knowledge's 209: 199: 121: 116: 115: 114: 91: 61: 12: 11: 5: 2585: 2583: 2575: 2574: 2569: 2564: 2559: 2554: 2549: 2544: 2539: 2534: 2529: 2524: 2519: 2514: 2509: 2504: 2494: 2493: 2476: 2473: 2461:Janyahmercedes 2427: 2424: 2381: 2378: 2359: 2356: 2335: 2334: 2327: 2280: 2279: 2271:Added archive 2249: 2246: 2210: 2204: 2199: 2193: 2188: 2183: 2179: 2172: 2168: 2164: 2158: 2153: 2148: 2144: 2139: 2135: 2131: 2127: 2124: 2119: 2114: 2109: 2105: 2101: 2080: 2076: 2072: 2068: 2063: 2057: 2052: 2047: 2043: 2036: 2032: 2028: 2024: 2020: 2014: 2009: 2004: 2000: 1995: 1973: 1969: 1964: 1958: 1953: 1948: 1944: 1937: 1933: 1928: 1923: 1918: 1914: 1890: 1885: 1880: 1876: 1872: 1869: 1865: 1842: 1822: 1818: 1805: 1802: 1796: 1795: 1767: 1764: 1747: 1744: 1743: 1742: 1699: 1696: 1679: 1676: 1662: 1661: 1658: 1655: 1650: 1647: 1646: 1645: 1601: 1598: 1583:simple machine 1571: 1568: 1567: 1566: 1551: 1546: 1545: 1513: 1510: 1509: 1508: 1465: 1462: 1461: 1460: 1433: 1397: 1396: 1382: 1363: 1362: 1348: 1347: 1338: 1337: 1332: 1331: 1294: 1291: 1289: 1286: 1270: 1267: 1251: 1248: 1228: 1225: 1224: 1223: 1191: 1188: 1172: 1171: 1135: 1132: 1131: 1130: 1115: 1112: 1094: 1091: 1066: 1063: 1046: 1043: 1016: 1013: 987: 984: 975: 974: 967: 963: 962: 948: 947: 940: 937: 933: 932: 915: 912: 886: 882: 880: 868: 865: 864: 863: 858: 840: 838: 834: 831: 820: 817: 816: 815: 814: 813: 800: 793: 792: 791: 790: 772: 771: 749:Franz Reuleaux 720: 717: 671: 670: 643: 636: 616: 604: 595: 592: 580:72.135.111.140 554: 551: 548: 547: 544: 543: 540: 539: 536: 526: 525: 514: 508: 507: 505: 488:the discussion 474: 462: 461: 446: 434: 433: 430: 429: 422:Top-importance 418: 412: 411: 409: 392:the discussion 379: 378: 375:Physics portal 362: 350: 349: 347:Top‑importance 341: 329: 328: 325: 324: 313: 307: 306: 304: 287:the discussion 274: 273: 257: 245: 244: 236: 224: 223: 217: 195: 181: 180: 118: 117: 113: 112: 107: 102: 93: 92: 90: 89: 82: 77: 68: 62: 60: 59: 48: 39: 38: 35: 34: 28: 13: 10: 9: 6: 4: 3: 2: 2584: 2573: 2570: 2568: 2565: 2563: 2560: 2558: 2555: 2553: 2550: 2548: 2545: 2543: 2540: 2538: 2535: 2533: 2530: 2528: 2525: 2523: 2520: 2518: 2515: 2513: 2510: 2508: 2505: 2503: 2500: 2499: 2497: 2490: 2489: 2485: 2481: 2474: 2472: 2470: 2466: 2462: 2456: 2454: 2450: 2446: 2433: 2425: 2423: 2422: 2418: 2414: 2408: 2405: 2402: 2399: 2395: 2392: 2389: 2386: 2379: 2377: 2376: 2372: 2368: 2365: 2357: 2355: 2354: 2349: 2344: 2343: 2332: 2328: 2325: 2321: 2320: 2319: 2312: 2306: 2302: 2298: 2294: 2288: 2283: 2278: 2274: 2270: 2269: 2268: 2266: 2262: 2258: 2253: 2247: 2245: 2243: 2239: 2235: 2231: 2227: 2221: 2208: 2202: 2197: 2191: 2181: 2170: 2166: 2162: 2156: 2146: 2137: 2133: 2125: 2117: 2107: 2091: 2078: 2070: 2066: 2061: 2055: 2045: 2034: 2030: 2022: 2018: 2012: 2002: 1993: 1984: 1971: 1967: 1962: 1956: 1946: 1935: 1931: 1926: 1916: 1903: 1888: 1878: 1870: 1867: 1854: 1840: 1820: 1803: 1801: 1793: 1789: 1784: 1781: 1779: 1774: 1765: 1763: 1762: 1758: 1754: 1753:Prof McCarthy 1745: 1741: 1737: 1733: 1732:Prof McCarthy 1729: 1728: 1727: 1724: 1720: 1716: 1712: 1708: 1697: 1695: 1694: 1690: 1686: 1685:Prof McCarthy 1677: 1675: 1674: 1670: 1666: 1659: 1656: 1653: 1652: 1648: 1644: 1640: 1636: 1631: 1630:the talk page 1627: 1622: 1619: 1618: 1617: 1616: 1612: 1608: 1607:Prof McCarthy 1599: 1597: 1596: 1592: 1588: 1584: 1580: 1579: 1569: 1565: 1561: 1557: 1552: 1548: 1547: 1542: 1541: 1540: 1539: 1535: 1531: 1530:Prof McCarthy 1523: 1518: 1511: 1507: 1503: 1499: 1495: 1490: 1489: 1488: 1487: 1483: 1479: 1478:Prof McCarthy 1470: 1463: 1459: 1455: 1451: 1447: 1443: 1439: 1434: 1430: 1426: 1422: 1418: 1414: 1413: 1412: 1411: 1407: 1403: 1402:Prof McCarthy 1395: 1391: 1387: 1383: 1380: 1379: 1378: 1377: 1373: 1369: 1368:Prof McCarthy 1361: 1357: 1353: 1350: 1349: 1345: 1340: 1339: 1334: 1333: 1329: 1325: 1320: 1319: 1318: 1317: 1313: 1309: 1308:Prof McCarthy 1299: 1287: 1285: 1284: 1280: 1276: 1275:Prof McCarthy 1268: 1266: 1265: 1261: 1257: 1256:Prof McCarthy 1249: 1247: 1246: 1242: 1238: 1237:Prof McCarthy 1234: 1226: 1222: 1218: 1214: 1213:Prof McCarthy 1209: 1208: 1207: 1206: 1202: 1198: 1197:Prof McCarthy 1189: 1187: 1186: 1182: 1178: 1177:Prof McCarthy 1170: 1166: 1162: 1161:Prof McCarthy 1157: 1156: 1155: 1154: 1150: 1146: 1145:Prof McCarthy 1142: 1133: 1129: 1126: 1122: 1118: 1117: 1111: 1109: 1105: 1101: 1092: 1090: 1089: 1085: 1081: 1077: 1073: 1070: 1064: 1062: 1061: 1057: 1053: 1044: 1042: 1040: 1036: 1032: 1028: 1024: 1014: 1012: 1010: 1006: 1002: 1001:78.21.233.253 998: 994: 985: 983: 982: 979: 972: 968: 965: 964: 960: 959: 958: 956: 952: 945: 941: 938: 935: 934: 930: 929: 928: 927: 924: 920: 913: 911: 909: 905: 901: 897: 890: 878: 877: 874: 866: 861: 859: 857: 854: 850: 849: 848: 847: 844: 832: 830: 829: 826: 818: 812: 808: 804: 801: 797: 796: 795: 794: 788: 784: 780: 776: 775: 774: 773: 770: 766: 762: 758: 754: 750: 746: 745: 740: 739: 738: 736: 732: 729: 725: 718: 716: 715: 711: 707: 701: 699: 695: 691: 687: 680: 679: 676: 669: 666: 661: 657: 653: 649: 642: 635: 631: 630: 629: 628: 625: 620: 614: 613: 610: 609:MarcusMaximus 605: 602: 599: 593: 591: 589: 585: 581: 577: 570: 569: 565: 561: 560:129.78.64.101 552: 532: 528: 527: 523: 519: 513: 510: 509: 506: 489: 485: 481: 480: 475: 472: 468: 467: 463: 450: 447: 444: 440: 427: 423: 417: 414: 413: 410: 393: 389: 385: 384: 376: 370: 365: 363: 360: 356: 355: 351: 345: 342: 339: 335: 322: 318: 317:High-priority 312: 309: 308: 305: 288: 284: 280: 279: 271: 265: 260: 258: 255: 251: 250: 246: 242:High‑priority 240: 237: 234: 230: 225: 221: 215: 207: 206: 196: 192: 187: 186: 177: 173: 170: 167: 163: 159: 155: 152: 149: 146: 143: 140: 137: 134: 131: 127: 124: 123:Find sources: 120: 119: 111: 110:Verifiability 108: 106: 103: 101: 98: 97: 96: 87: 83: 81: 78: 76: 72: 69: 67: 64: 63: 57: 53: 52:Learn to edit 49: 46: 41: 40: 37: 36: 32: 26: 22: 18: 17: 2478: 2457: 2429: 2409: 2406: 2403: 2400: 2396: 2393: 2390: 2387: 2383: 2361: 2339: 2336: 2311:source check 2290: 2284: 2281: 2254: 2251: 2224:— Preceding 2222: 2092: 1985: 1904: 1855: 1807: 1799: 1769: 1749: 1705:— Preceding 1701: 1681: 1663: 1654:Read through 1603: 1576: 1573: 1526: 1475: 1441: 1437: 1428: 1424: 1420: 1416: 1398: 1364: 1324:steam engine 1304: 1272: 1253: 1230: 1193: 1173: 1137: 1096: 1093:"Kinematics" 1080:91.51.204.80 1078: 1074: 1071: 1068: 1052:NarSakSasLee 1050:pronounced? 1048: 1018: 1015:Broken Links 996: 992: 989: 976: 950: 949: 925: 922: 921: 917: 891: 879: 870: 836: 822: 753:Introduction 742: 731:September 24 726: 722: 702: 681: 672: 659: 655: 651: 647: 640: 633: 615: 606: 603: 600: 597: 571: 556: 517: 477: 421: 381: 316: 276: 220:WikiProjects 203: 171: 165: 157: 150: 144: 138: 132: 122: 94: 19:This is the 1786:Adopted by 1626:WP:Refactor 1021:—Preceding 944:unit vector 894:—Preceding 803:Bkpsusmitaa 684:—Preceding 646:instead of 574:—Preceding 292:Mathematics 283:mathematics 239:Mathematics 148:free images 31:not a forum 2496:Categories 2348:Report bug 2257:Kinematics 1665:Chaosdruid 961:Sublevels: 955:rigid body 931:Sublevels: 747:(1876) by 737:21:22 UTC 25:Kinematics 2331:this tool 2324:this tool 1790:from the 1678:Revisions 1446:this edit 873:Jhausauer 783:talk page 675:Anonymous 208:is rated 88:if needed 71:Be polite 21:talk page 2367:Admazzeo 2337:Cheers.— 2238:contribs 2226:unsigned 1719:contribs 1707:unsigned 1635:Paolo.dL 1587:Paolo.dL 1556:Paolo.dL 1498:Paolo.dL 1450:Paolo.dL 1386:Paolo.dL 1352:Paolo.dL 1035:contribs 1023:unsigned 978:Paolo.dL 896:unsigned 867:notation 706:M0nstr42 686:unsigned 665:Tgilro01 576:unsigned 493:Robotics 484:Robotics 449:Robotics 56:get help 29:This is 27:article. 2261:my edit 1121:Peacock 785:of the 520:on the 424:on the 397:Physics 388:Physics 344:Physics 319:on the 210:B-class 154:WP refs 142:scholar 2230:Nooser 1788:Willow 1657:Assess 1344:WP:MOS 1027:Jwedes 779:Dhskep 728:Dhskep 216:scale. 126:Google 1464:Wheel 843:Eps0n 197:This 169:JSTOR 130:books 84:Seek 2484:talk 2465:talk 2439:and 2417:talk 2371:talk 2234:talk 1757:talk 1736:talk 1715:talk 1689:talk 1669:talk 1639:talk 1611:talk 1591:talk 1560:talk 1534:talk 1502:talk 1482:talk 1454:talk 1421:your 1406:talk 1390:talk 1372:talk 1356:talk 1312:talk 1279:talk 1260:talk 1241:talk 1217:talk 1201:talk 1181:talk 1165:talk 1149:talk 1125:Lane 1104:talk 1084:talk 1056:talk 1031:talk 1005:talk 904:talk 885:or v 807:talk 765:talk 735:2006 710:talk 694:talk 658:and 650:and 639:and 584:talk 564:talk 512:High 311:High 162:FENS 136:news 73:and 2455:). 2305:RfC 2275:to 1438:our 1326:or 957:). 853:HEL 825:HEL 761:LA2 416:Top 176:TWL 2498:: 2486:) 2467:) 2419:) 2373:) 2318:. 2313:}} 2309:{{ 2240:) 2236:• 2167:∘ 2147:− 2126:∘ 2108:− 2071:∘ 2023:∘ 2003:− 1917:− 1879:− 1853:: 1759:) 1738:) 1721:) 1717:• 1691:) 1671:) 1641:) 1613:) 1593:) 1562:) 1536:) 1504:) 1484:) 1456:) 1448:. 1442:my 1429:us 1425:we 1408:) 1392:) 1374:) 1358:) 1314:) 1281:) 1262:) 1243:) 1219:) 1203:) 1183:) 1167:) 1151:) 1106:) 1086:) 1058:) 1037:) 1033:• 1007:) 991:'d 906:) 809:) 767:) 733:, 712:) 696:) 622:-- 586:) 566:) 156:) 54:; 2482:( 2463:( 2451:( 2415:( 2369:( 2350:) 2346:( 2333:. 2326:. 2232:( 2209:, 2203:) 2198:2 2192:0 2187:V 2182:+ 2178:V 2171:( 2163:) 2157:0 2152:V 2143:V 2138:( 2134:= 2130:A 2123:) 2118:0 2113:P 2104:P 2100:( 2079:t 2075:A 2067:) 2062:2 2056:0 2051:V 2046:+ 2042:V 2035:( 2031:= 2027:A 2019:) 2013:0 2008:P 1999:P 1994:( 1972:t 1968:) 1963:2 1957:0 1952:V 1947:+ 1943:V 1936:( 1932:= 1927:0 1922:P 1913:P 1889:0 1884:V 1875:V 1871:= 1868:t 1864:A 1841:t 1821:t 1817:A 1794:. 1755:( 1734:( 1713:( 1687:( 1667:( 1637:( 1609:( 1589:( 1558:( 1532:( 1500:( 1480:( 1452:( 1417:I 1404:( 1388:( 1370:( 1354:( 1330:. 1310:( 1277:( 1258:( 1239:( 1215:( 1199:( 1179:( 1163:( 1147:( 1123:. 1102:( 1082:( 1054:( 1029:( 1003:( 997:t 993:s 973:) 902:( 887:i 883:0 881:v 862:] 805:( 763:( 708:( 692:( 660:u 656:v 652:u 648:v 644:f 641:v 637:i 634:v 582:( 562:( 524:. 428:. 323:. 222:: 172:· 166:· 158:· 151:· 145:· 139:· 133:· 128:( 58:.

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

Index