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= March 29 =

==bird ID==
[[File:Malasari elang.jpg|thumb|]]
What bird is this? The file id's it as a [[Javan hawk-eagle]] but I think it looks more like a [[black eagle]]. Said to be photographed in [[Mount Halimun Salak National Park]] on Java where 10 Javan hawk-eagles are said to have been found. [[User:Rmhermen|Rmhermen]] ([[User talk:Rmhermen|talk]]) 01:51, 29 March 2016 (UTC)

:Yes, it does look more like the black eagle.  While the black eagle isn't listed as being native to [[Java]], it does extend down to the [[Malay Peninsula]].  I wonder if that would put them close enough to be within flight distance (they could stop off at [[Sumatra]] on the way).  [[User:StuRat|StuRat]] ([[User talk:StuRat|talk]]) 03:37, 29 March 2016 (UTC)

::It does look ''more like'' the black eagle (not a terribly high bar as the pictured bird is pretty clearly not a Javan hawk-eagle), but I'm not so sure that's what it is; the barring on the tail is rather distinctly different. Note: I'm no expert; that could easily be due to normal variation. [[User:Matt Deres|Matt Deres]] ([[User talk:Matt Deres|talk]]) 15:20, 30 March 2016 (UTC)

== In fact indeed do exist a real uni-polar neuron? ==
[[File:Neurons_uni_bi_multi_pseudouni.svg|thumb|'''Different kinds of neurons''': '''1''' Unipolar neuron '''2''' Bipolar neuron '''3''' Multipolar neuron '''4''' Pseudounipolar neuron]]
According to the [[Neuron#/media/File:Neurons_uni_bi_multi_pseudouni.svg|article on Wikipedia]], do exist real uni-polar neuron ans this is in contrast (apparently) to what I saw in the books that I read that there are three is only pseoudo-unipolar neuron. So in fact indeed do exist a real uni-polar neuron? [[Special:Contributions/93.126.95.68|93.126.95.68]] ([[User talk:93.126.95.68|talk]]) 02:32, 29 March 2016 (UTC)
:Yes, there are real unipolar neurons.  They are very common in insects and other invertebrates but also exist in vertebrates.  If you are asking anything more, I can't understand it. [[User:Looie496|Looie496]] ([[User talk:Looie496|talk]]) 00:58, 30 March 2016 (UTC)
::I'm not even sure why they is asking, as in order to link us that picture, they had to have seen the article explaining that they are real and what they are. --[[User:OuroborosCobra|OuroborosCobra]] ([[User talk:OuroborosCobra|talk]]) 01:49, 30 March 2016 (UTC)

== Special relativity. Simultaneity ==
{| class="wikitable" style="width:100%"
|-
! Question
! Remark
|-
| As [[User:BenRG|BenRG]] ([[User talk:BenRG|talk]]) 17:39, 20 March 2016 (UTC) said here https://en.wikipedia.org/enwiki/w/index.php?title=Wikipedia:Reference_desk/Science&action=edit&oldid=711808143, digital displays cannot lie. But as we know from Special relativity , clocks in moving reference frame are not synchronized. E.g. our clock shows <math>t \sec</math> from Big Bang (or from any other moment). Another frame passing us with speed <math>\mathbf u</math> has 3 clocks: front-end, hind-end and middle clock. When middle clock passing our clock , our clock and middle clock are synchronized manually. Man in moving frame synchronizes front-end and hind-end clocks with middle manually. Then we see from our frame:

our clock shows <math>t \sec</math>;

middle clock shows <math>t \sec</math>;

front-end clock shows <math>t - 4 \sec</math>;

hind-end clock shows <math>t + 4 \sec</math>.

When moving reference frame will stop instantly (<math>a=-\infty</math>), what will we see on front-end and hind-end clocks and why?
| https://en.wikipedia.org/enwiki/w/index.php?title=Wikipedia:Reference_desk/Science&action=edit&oldid=711808143 [[Null result of Michelson–Morley experiment extrapolation]]

https://archive.org/download/PhysicsForTheEnquiringMind/Rogers-PhysicsForTheEnquiringMind.djvu , page 492
|}
[[Special:Contributions/37.53.235.112|37.53.235.112]] ([[User talk:37.53.235.112|talk]]) 05:04, 29 March 2016 (UTC)

:You've specified that the moving clocks differ by 4 seconds when measured simultaneously [[wikt:WRT|wrt]] the lab frame, and I'll assume that they all stop simultaneously wrt the lab frame. Then after stopping they will still differ by 4 seconds wrt the lab frame, because acceleration doesn't affect ideal clocks; their reading doesn't jump forward or backward at the moment of the acceleration, they just keep ticking. This is an example of ideal clocks losing their synchronization when accelerated, which happens in special relativity but not in Newtonian physics. (Another example is the twin paradox/effect: the twins' initially synchronized ages are desynchronized when they meet again.) -- [[User:BenRG|BenRG]] ([[User talk:BenRG|talk]]) 05:59, 29 March 2016 (UTC)
::When moving ref. frame stops, it merges with ours. Man from moving frame saw clocks sinchronized. An when his frame will stop he will see difference, or what? But digital display can't do such things.[[Special:Contributions/37.53.235.112|37.53.235.112]] ([[User talk:37.53.235.112|talk]]) 10:30, 29 March 2016 (UTC)
:::The clocks are just clocks. They aren't aware of each other, they just follow their own local laws. If they end up not Einstein-synchronized, and you still want to call them a reference frame, that's fine as long as you're willing to accept the consequences (more complicated-looking physical laws), but the universe doesn't care one way or another what you use as a reference frame. -- [[User:BenRG|BenRG]] ([[User talk:BenRG|talk]]) 19:58, 29 March 2016 (UTC)

Could someone clearly and simply state what's being asked here? I can't figure it out...but find the topic interesting so would like to understand what's being discussed...[[Special:Contributions/68.48.241.158|68.48.241.158]] ([[User talk:68.48.241.158|talk]]) 15:26, 29 March 2016 (UTC)
:I think you need first check links in Remark column. Don't worry, 99% of people don't understand special relativity.[[Special:Contributions/37.53.235.112|37.53.235.112]] ([[User talk:37.53.235.112|talk]]) 16:47, 29 March 2016 (UTC)

:I think the question is simply whether, if you accelerate a bunch of comoving [[Einstein synchronisation|Einstein-synchronized]] clocks, they will still be Einstein-synchronized afterwards. The answer is no in general (yes in special cases, but the question wasn't about one of those cases). -- [[User:BenRG|BenRG]] ([[User talk:BenRG|talk]]) 19:58, 29 March 2016 (UTC)

{| class="wikitable" style="width:100%"
|-
! Question
! Remark
|-
| Another question. Suppose we have 2 observers ε (at rest) and ε' (moving) in 2 coaches as on Fig. 31-39 :
https:/upwiki/wikipedia/commons/1/17/160329155625UTC.png

Observer ε has 1 clock, it shows time in frame ε:
*at start <math>0</math>, 
*when ligth raeches hind end of ε' coach <math>\tau_1</math>,
*when ligth raeches front end of ε' coach <math>\tau_2</math>.

Also observer ε can see ε' clocks (ε' has 3 clocks hind, middle, front) from frame ε:
*at start ε' clocks shows <math>\theta_0^{[}</math> ([ means hind end),  <math>0</math> (at start observers sinchronized clocks manually),  <math>\theta_0^{]}</math> (] means front end), 
*when ligth raeches hind end of ε' coach <math>\theta_1^{[}</math>,  <math>\theta_1</math>,  <math>\theta_1^{]}</math>, 
*when ligth raeches front end of ε' coach <math>\theta_2^{[}</math>,  <math>\theta_2</math>,  <math>\theta_2^{]}</math>.

First let us find <math>\tau_1</math> and <math>\tau_2</math>:

<math>\tau_1=\tfrac{L/2}{c+u}; \tau_2=\tfrac{L/2}{c-u}</math>.

Then , suppose <math>\theta_1^{[} = \theta_2^{]}</math>. 
We have:

<math>\theta_1^{[} = \theta_0^{[} + \tau_1\sqrt{1-u^2/c^2}</math>, <math>\theta_2^{]} = \theta_0^{]} + \tau_2\sqrt{1-u^2/c^2}</math>, so


<math>\theta_0^{[} + \tau_1\sqrt{1-u^2/c^2} = \theta_0^{]} + \tau_2\sqrt{1-u^2/c^2}</math>;


<math>\theta_0^{[} - \theta_0^{]}  =  \tau_2\sqrt{1-u^2/c^2} - \tau_1\sqrt{1-u^2/c^2}</math>

<math>=  \sqrt{1-u^2/c^2}(\tau_2 - \tau_1)</math>

<math>=  \sqrt{1-u^2/c^2}(\tfrac{L/2}{c-u} - \tfrac{L/2}{c+u})</math>

<math>=  \sqrt{1-u^2/c^2}\tfrac{Lu/c^2}{1-u^2/c^2}</math>

<math>=  \tfrac{Lu/c^2}{\sqrt{1-u^2/c^2}} = \tfrac{(x^{]}-x^{[})u/c^2}{\sqrt{1-u^2/c^2}}</math> .

<b>First ,</b> why do we suppose <math>\theta_1^{[} = \theta_2^{]}</math>? These times do match only in ε' frame as observer ε' sinchronized all his clocks. <math>\theta_{0,self}^{[} = \theta_{0,self} = \theta_{0,self}^{]} = 0</math>. When light reaches walls in frame ε': <math>\theta_{self}^{[} = \theta_{self} = \theta_{self}^{]} = \tfrac{L/2}{c}</math>. https:/upwiki/wikipedia/commons/4/49/160329181132UTC.PNG

<b>Second.</b> <math>\theta_1</math> and <math>\theta_2</math> are not used, but are next eq. correct <math>\theta_1 = \tau_1\sqrt{1-u^2/c^2}</math>, <math>\theta_2 = \tau_2\sqrt{1-u^2/c^2}</math> ? Should we not make correction for coordinate term <math>ux/c^2</math>? 

<b>Third.</b> What actually is <math>t'</math> from Lorentz transformations ?  Time interval or moment time or what?

<math>t' = \tfrac{t-ux/c^2}{\sqrt{1-u^2/c^2}}</math>

If <math>x=0</math> then <math>t' = \tfrac{t}{\sqrt{1-u^2/c^2}}</math>. So <math>t' > t</math>, as <math>\sqrt{1-u^2/c^2}<1</math> and so <math>\tfrac{1}{\sqrt{1-u^2/c^2}}>1</math>. But we know that time goes slower in moving frame, so we always have <math>t' \sec < t \sec</math>.

| https://archive.org/download/PhysicsForTheEnquiringMind/Rogers-PhysicsForTheEnquiringMind.djvu , page 493, Fig. 31-39.
http://www.feynmanlectures.caltech.edu/I_15.html#Ch15-S6
|}
[[Special:Contributions/37.53.235.112|37.53.235.112]] ([[User talk:37.53.235.112|talk]]) 16:47, 29 March 2016 (UTC)

:Is the observer actually "seeing"/detecting light from three clocks that (at the moment) displays +4, 0, -4?  Or are there three observers that happen to be beside the three moving clocks, at rest relative to one another, who at the same moment (from their perspective) see these readings and later communicate them?  In the second case,  instantaneous deceleration should not much affect the clock reading as said above.  But in the first case, light emitted by the clocks will continue to tick forward after the deceleration, showing them keeping time at a different rate due to time dilation; once the deceleration happens they tick at normal speed.  But exactly ''when'' the deceleration occurs, there's a bit of a mystery; bear in mind that if the three clocks decelerate at the same time in your frame of reference, that's a different time in theirs, which is why the Lorentz contraction becomes a ''real'' crunching together in space (as it must for the Lorentz contracted object all to stop at the same time as you see it). [[User:Wnt|Wnt]] ([[User talk:Wnt|talk]]) 18:14, 29 March 2016 (UTC)
::<span style="color:#999999;">Is the observer actually "seeing"/detecting light from three clocks that (at the moment) displays +4, 0, -4?  Or are there three observers that happen to be beside the three moving clocks</span> -- As in E.Rogers book [page 493, note 19], I think observer at rest allows for time-delay of seeing a clock that is far away. To do that he can use 2 helpers or put 2 additional clocks, yes. But question isn't with observer at rest, but with both observers. Before stop moving observer sees 0, 0, 0. Observer at rest sees +4, 0, -4. After stop observer at rest still sees +4, 0, -4. Stoped observer sees ... what? also +4, 0, -4? [[Special:Contributions/37.53.235.112|37.53.235.112]] ([[User talk:37.53.235.112|talk]]) 18:39, 29 March 2016 (UTC)
::: The stopped observer sees one clock stop at -4, then he keeps going on for a while and stops later, then the last clock keeps moving at him and then stops at +4.  Note that the actual difference in time is generally small and the distance large - you would never see a [[timelike]] slice of someone else's [[light cone]] in normal space at any speed - so there is always enough distance for the clocks to tick that far before they change speed. [[User:Wnt|Wnt]] ([[User talk:Wnt|talk]]) 10:18, 30 March 2016 (UTC)

:I urge you to forget about "observers". The experiment here consists of the train car, the light, and the clocks. There needs to be an experimenter looking at the digital readouts of the clocks, but that person doesn't need to be moving in any particular way, doesn't need to look only at certain clocks and ignore others, etc.
:To answer your third question first, <math>t'</math> is a coordinate. You're probably familiar with Cartesian coordinates from Euclidean geometry, and you know that the transformation between different coordinate systems (with a common origin) looks like
::<math>x' = x \cos \theta - y \sin \theta</math>
::<math>y' = y \sin \theta + x \cos \theta</math>
:where <math>\theta</math> is the angle between (say) the x axes. There's no reason we have to use the ''angle''; we could instead use the ''slope'' of one x axis with respect to the other coordinate system. Call the slope <math>v</math>. Then <math>\theta = tan^{-1} v</math>, and plugging that in and doing some trig substitutions gives you
::<math>x' = \gamma (x - v y)</math>
::<math>y' = \gamma (y + v x/c^2)</math>
:where <math>\gamma = 1/\sqrt{1+v^2/c^2}</math> and <math>c=1</math>. The reason this looks almost the same as the Lorentz transform is that they are almost the same thing. The similarity is hidden by the completely arbitrary way in which special relativity has always been taught. By convention, we use the slope <math>v</math> between the coordinate systems instead of the [[rapidity|angle]] <math>\alpha</math>. By convention, we use different units for distance and time intervals, which necessitates adding in some factors of <math>c</math>. None of this accomplishes anything; the universe doesn't care. Time is actually just another dimension, and the Lorentz transformation is just a coordinate transformation.
:When you transform Cartesian coordinates, you plug in the coordinates of a point (x,y), and get new ''coordinates'' of the ''same'' point, (x',y'). Either pair of coordinates, by itself, identifies the point. You don't need both pairs. You don't need to pick the coordinate system that the point is "in". All points are "in" all coordinate systems. You should pick the coordinate system that's most convenient for the problem you're trying to solve. Any coordinate system will work, because they're equivalent descriptions of the same geometry.
:Coordinate pairs like (x,y) or (x',y') must always be kept together because the components are meaningless by themselves. An equation like x=3 can define a line, but if you want to transform that equation into a different coordinate system, you can't just plug the x coordinate into the transformation equations and get an x'. The line doesn't have an equation of the form x'=anything. You can, for example, write the line parametrically as x(q) = 3, y(q) = q, or better as (x,y)(q) = (3,q), and plug the pairs (3,q) into the coordinate transformation, and get a correct parametric equation for the line in terms of the other coordinates. Likewise, pairs like (x,t) and (x',t') must be kept together. You can't just transform time. You must always use both (or all four) of the Lorentz transformation equations together, otherwise you will get nonsensical results (unless you really understand what you're doing).
:In your problem, say the light is emitted at (0,0) (in either coordinate system). It reaches the walls at <math>(x',t') = (\pm L/2, L/2c)</math>, or equivalently <math>(x,t) = (\tfrac{\pm Lc}{2(c\pm u)}, \tfrac{L}{2(c\pm u)})</math>. Your first clock has the parametric equation (x,t)(τ) = (0,τ), which you can plug into the Lorentz transformation to find (x',t')(τ). To find the digital reading of that clock at a particular (x,t) or (x',t'), you just solve for τ. Your other three clocks have the parametric equations (x',t')(θ) = (0, θ) and (x',t')(θ<sup>[]</sup>) = (±L/2, θ<sup>[]</sup>), and you can plug those into the Lorentz transformation to find (x,t)(θ<sup>whatever</sup>). Any question you have about what someone sees at a given (place,time) can be answered in this way. They are simple questions about [[coordinate geometry]]. -- [[User:BenRG|BenRG]] ([[User talk:BenRG|talk]]) 19:58, 29 March 2016 (UTC)

::Last Sunday, March 27, 2016 we had to put our beloved cat to sleep. She was 21 and sick for a year. She weighed only 4 pounds with her premorbid weight of 12 pounds, skin and bones. She could not eat at all for the last week or so. She lived with us for 18 years. Two weeks before she died our long-functioning wall clock stopped and it seems we must throw it out. On Monday I found out to my surprise that it is a common belief that if your clock stopped, somebody will die in your family and this cat was a true family member. It is a true story. Read this Daily Mail [http://www.dailymail.co.uk/news/article-2634427/Each-time-one-relatives-died-clock-stopped-Just-one-haunting-stories-Mail-readers-tell-experiences-ghostly-events-surrounding-deaths-families.html article]. Is it a Special Relativity or what? --[[User:AboutFace 22|AboutFace 22]] ([[User talk:AboutFace 22|talk]]) 22:11, 29 March 2016 (UTC)
{| class="wikitable" style="width:100%"
|-
! Question
! Quote
|-
| So <math>(x',t')(\tau)</math> are space-time coordinates of 1st clock in rest frame seen from moving frame, right?

<math>(x',t')(\tau) = (\tfrac{x-ut}{\sqrt{1-u^2/c^2}} ; \tfrac{t-ux/c^2}{\sqrt{1-u^2/c^2}})</math>

<math>(x',t')(\tau) = (\tfrac{0-u\tau}{\sqrt{1-u^2/c^2}} ; \tfrac{\tau-0}{\sqrt{1-u^2/c^2}})</math>

At time <math>\tau_1</math> 1st clock will show <math>(x',t')(\tau_1) = (\tfrac{-u\tau_1}{\sqrt{1-u^2/c^2}} ; \tfrac{\tau_1}{\sqrt{1-u^2/c^2}})</math>, seen from moving ε' frame. Is it correct?

Thank you. But I will study Special relativity as rotatings next month. Now I must understand all without coordinates, angles, etc. I follow Feynman Lectures and chapters 15-1...15-6 don't use rotatings.
| <span style="color:#999999;">In your problem, say the light is emitted at (0,0) (in either coordinate system). It reaches the walls at <math>(x',t') = (\pm L/2, L/2c)</math>, or equivalently <math>(x,t) = (\tfrac{\pm Lc}{2(c\pm u)}, \tfrac{L}{2(c\pm u)})</math>. Your first clock has the parametric equation (x,t)(τ) = (0,τ), which you can plug into the Lorentz transformation to find (x',t')(τ). To find the digital reading of that clock at a particular (x,t) or (x',t'), you just solve for τ.</span> 
|}[[Special:Contributions/37.53.235.112|37.53.235.112]] ([[User talk:37.53.235.112|talk]]) 09:05, 30 March 2016 (UTC)

:{{tq|So <math>(x',t')(\tau)</math> are space-time coordinates of 1st clock in rest frame seen from moving frame, right?}} – <math>(x,t)(\tau)</math> is where the clock actually is, and <math>(x',t')(\tau)</math> is also where the clock actually is, just expressed in a different way. To figure out what people see, you need to trace light from the clock to someone's eye (and you can use either coordinate system to do that, and get the same result, since they describe the same world).
:{{tq|At time <math>\tau_1</math> 1st clock will show <math>(x',t')(\tau_1) = (\tfrac{-u\tau_1}{\sqrt{1-u^2/c^2}} ; \tfrac{\tau_1}{\sqrt{1-u^2/c^2}})</math>, seen from moving ε' frame. Is it correct?}} – I think the algebra is right, but the description is sort of backwards. The clock shows <math>\tau_1</math> on its face when it's at <math>(x',t') = (\tfrac{-u\tau_1}{\sqrt{1-u^2/c^2}}, \tfrac{\tau_1}{\sqrt{1-u^2/c^2}})</math>. -- [[User:BenRG|BenRG]] ([[User talk:BenRG|talk]]) 17:20, 31 March 2016 (UTC)

== Kinetic energy of charged particles ==

What is the expression of the kinetic energy of moving [[charged particle]]s?--[[Special:Contributions/5.2.200.163|5.2.200.163]] ([[User talk:5.2.200.163|talk]]) 15:38, 29 March 2016 (UTC)

:You'll need to provide more context.  In many cases, the classical formula - the one you probably know as <math>KE = 1/2 m v^2</math> - is good enough for the job.  In [http://www.pearsonhighered.com/educator/product/Introduction-to-Electrodynamics/9780321856562.page Griffith's book], he advances the definition to account for special relativity, using the formuka <math>E_{kin} = m c^2 ( \frac{1}{\sqrt{1-\frac{u^2}{c^2}}}-1)</math> for relativistic velocity ''u''.  In [http://www.springer.com/us/book/9780387209753 Bittencourt's book], which makes extensive use of energy analysis for charged particles, the author uses a more statistical approach, defining an ''energy density'' just for kinetic energy: <math>W_\alpha = 1/2 \rho_{m \alpha} u_{\alpha}^2 + 1/2 \rho_{m \alpha} <c_{\alpha}^2></math> for the ''mean kinetic energy density'' of particles of species α, mass density ρ, with velocity ''u'' and ''peculiar velocity'' ''c'' (representing sort of "[[Brownian motion]]" separately from bulk particle transport velocity).  The author proceeds to analyze other statistical measures of the kinetic energy distribution - there's more information than just the average value!  In a sense, this is a ''classical'' treatment: so if you wanted to deal with something awful, like a multi-species, hot, dense, relativistic plasma, with each charged specie interacting with every other charged specie - say, modeling the charged particles inside the sun or inside a nuclear bomb - you'd have to synthesize a corrected ''total energy'' and ''total kinetic energy'' equation that combines a lot more terms and forms!
:Many times, especially in quantum mechanics, kinetic energy is [[Kinetic_energy#Kinetic_energy_in_quantum_mechanics|defined as an operator]], and is usually expressed in relation to the momentum (not the mass and velocity).  This is particularly helpful when ''laboratory measurement'' of mass or velocity is muddied by technical difficulties: for example, it is often easier to measure the ''energy'' of a charged particle than to measure its mass, charge, or velocity: we have lots of machines that can directly measure electron energy, like an [[electron spectrometer]] or an [[Electron energy loss spectroscopy|electron energy loss spectrum analyzer]].
:The point is, lots of advanced physics just builds on top of the basic physics you already know, and adds complications one step at a time.
:[[User:Nimur|Nimur]] ([[User talk:Nimur|talk]]) 16:01, 29 March 2016 (UTC)
::More context would be connected to what the article [[momentum#Electromagnetism#Particle in field]] says and the relation between kinetic energy and momentum within electromagnetism.--[[Special:Contributions/5.2.200.163|5.2.200.163]] ([[User talk:5.2.200.163|talk]]) 16:39, 29 March 2016 (UTC)
:::If you look closely at the subsection you linked, you can see that the first row of the first column contains a classical kinetic energy term, in vector coordinates.  The next column applies a [[Lorentz transform]] to that equation.  The trick to extract the ''kinetic energy'' term is to carefully observe and recognize its general form.  If you make simplifying assumptions, the equation is exactly the same as the one you learn in basic physics.  You can go ''very far'' with Newtonian-style equations - and unless you like making extra work for yourself, in many cases you ''should'' use the simplest form of the equation.
:::But, the authors of the section you linked are being very cautious in order to be ''generally correct.''  For example, they write <math>\frac{m}{2}\mathbf{\dot{r}}\cdot\mathbf{\dot{r}}</math> instead of <math>\frac{m}{2} v^2</math>.  Why have they written it in this way?
:::Can you think of any condition in which the time derivative of the position vector is not the strict ''velocity'' vector?  Or, more likely: where would the inner product of the time derivative of the position vector, multipled by itself, not be equal to the square of the scalar velocity?
:::I can think of a case: a non-[[scleronomous]] coordinate system - like the swinging arm of a [[double pendulum]] (or, in electrodynamics: a charged particle orbiting an ''accelerating charged particle'' - like we might see in the electron of a ''nearly''-ionized hydrogen atom traveling in the [[van Allen belt]])!  We don't even have to dive deep into relativistic physics or quantum physics - just classical cases - where the general form of the equation is more correct.  Throw in the effects of relativity, or the wacky nonsense called "quantum mechanics," and the equations just get more and more complicated.  Yet, this allows us to solve equations of motion - and conserve energy, and so forth - even in non-inertial reference frames, or in cases of non-conservative forces, and so forth.
:::[[User:Nimur|Nimur]] ([[User talk:Nimur|talk]]) 17:47, 29 March 2016 (UTC)
::::Hey {{ping|Nimur}} are you saying that for a pendulum whose pivot undergoes simple harmonic oscillation, the equation <math>\frac{m}{2} v^2</math> does not yield the right answer for kinetic energy, but the r-dot form does (assuming both the v and r are with respect to the same non-moving frame in which the pivot oscillates)? Also, is "non-scleronomous" just a synonym for "[[rheonomous]]" in this case (or in general)? Both those articles could use some improvement... [[User:SemanticMantis|SemanticMantis]] ([[User talk:SemanticMantis|talk]]) 18:34, 29 March 2016 (UTC)
:::::The point is that a double pendulum provides an easy-to-visualize case of a complicated [[non-inertial reference frame]].  If you are not very careful about the definition of the ''position'' (and therefore, the ''velocity''), you end up computing very strange (incorrect!) quantities of energy.  For example: you can fully treat the double pendulum as a two-dimensional system; you may, therefore, represent the position of the end-effector as either Cartesian (x,y) pair, or you may use the angular position of each hinge (''θ<sub>1</sub>, θ<sub>2</sub>'').  Both representations are of equal [[Rank (linear algebra)|rank]], so they fully describe all the [[degrees of freedom]]; but if you use the ''x'', ''y'', position of the second segment of the arm, you are probably forgetting to account for the mass, momentum, and energy carried by the ''first'' segment of the arm - or you're setting yourself up for some ''terrible'' algebraic transforms!  One representation provides a much more natural way to represent and compute the kinetic energy. 
:::::Yes, [[rheonomous]] and [[scleronomous]] coordinate systems are opposites.  These terms show up in robotics, physics, and so on.  These terms refer to whether your [[generalized coordinates]] are time-invariant.
:::::You might also find [[holonomic constraints|holonomic]] and [[Nonholonomic system|non-holonomic coordinates]], especially [[Holonomic (robotics)|in the contexts of robotics]].  These terms refer to whether your generalized coordinates are orthogonal and whether they inherently depend on the time-history.
:::::[[User:Nimur|Nimur]] ([[User talk:Nimur|talk]]) 20:21, 29 March 2016 (UTC)

== Most abundant species? ==


[http://www.cracked.com/blog/6-animals-who-think-theyre-better-than-us/] and [http://www.cracked.com/blog/6-animals-who-think-theyre-better-than-us_p2/] makes the following claims:

(''Cracked'' is not a reliable source for anything but bad jokes, but they are right surprisingly often.)

* The Antarctic krill is the most abundant animal species, with a population of 500 trillion. I would have guessed nematodes or one of the bacteria. 
* Cows are the animal species with the highest total weight -- 170 million tons. I would have guessed one of the ant species.

Has anyone made an educated guess as to the most abundant species by number of individuals or by total weight? --[[User:Guy Macon|Guy Macon]] ([[User talk:Guy Macon|talk]]) 21:26, 29 March 2016 (UTC)

::if google 'total weight all ants' a bunch of articles will come up...apparently there's no scientific consensus as to how many ants there are on earth (like not even a good guess)...only that there are a lot....obviously too bacteria and such are not considered animals..[[Special:Contributions/68.48.241.158|68.48.241.158]] ([[User talk:68.48.241.158|talk]]) 21:36, 29 March 2016 (UTC)
:::What you are looking for is the animal with the largest [[biomass]], the article has a list. [[User:Vespine|Vespine]] ([[User talk:Vespine|talk]]) 00:05, 30 March 2016 (UTC)
::::Actually, the list is at [[Biomass (ecology)]] - the [[Biomass]] article is about plant crops used as a source of fuel. [[Special:Contributions/217.44.50.87|217.44.50.87]] ([[User talk:217.44.50.87|talk]]) 09:32, 30 March 2016 (UTC)

:Ants are commonly estimated to be roughly equal to human biomass. [[E.O. Wilson]] claims this in his book ''The Insect Societies'', and '''[http://www.antweb.org/antblog/2010/10/do-ants-really-have-the-largest-biomass-of-all-species-on-earth-laurie-usa.html here]''' is a nice discussion  of the claim, with further citations, and it also addresses the krill, with additional citation. Wilson and Holldobler have additionally estimated 10,000 ''trillion'' individual ants alive at a time, which would far surpass the krill. But maybe we're not making the right comparisons. The simple reason ants cannot be the most massive ''species'' is because their are many, many (>10k) species of ant; the [[Formicidae]] are a family. In contrast, we could probably claim that all the [[breed]]s of cattle still constitute a single species, and thus the cattle would out mass any single species of ant. Back to the krill, keep in mind they live in a much thicker layer than any other candidates on the list. Sure there are arboreal ants, and the nematodes go down a few feet maybe, but that's nothing compared the zone [[Antarctic krill]] inhabit, which is up to 3 km deep. Anyway, if you want to restrict to single ''species'', a specific ant is  probably not going to hold any records. If you want to compete all ranks, clades, and unranked groups then all the records are going to be set by one of the three [[Domain_(biology)|domains]]. [[User:SemanticMantis|SemanticMantis]] ([[User talk:SemanticMantis|talk]]) 13:37, 30 March 2016 (UTC)
::It's also worth noting that it is often claimed that 1/4th of all living things are [[beetles]]. (like [http://insects.about.com/od/beetles/a/10-Facts-About-Beetles.htm here])  However, that claim is usually based on the fact that about 1/4th of all identified ''species'' are beetle species, which is ''yet another way to count'' living things.  About 1/4th of all species are species we classify as beetle species.  Some will confuse this with the above definitions of "most", so while "ants" as a classification contain more individuals than "beetles" would, there are more different kinds of beetles than there are kinds of ants.  --[[User:Jayron32|<span style="color:#009">Jayron</span>]][[User talk:Jayron32|<b style="color:#090">''32''</b>]] 14:38, 30 March 2016 (UTC)
:::And just to emphasize it again, that's only ''described'' species. Amateur and semi-professional collecting of beetles goes back more than a century and the differences between beetles are rather easier to discern with the naked eye. In other words, more attention was historically paid to describing and cataloging beetles than ants, which skews the numbers. [[User:Matt Deres|Matt Deres]] ([[User talk:Matt Deres|talk]]) 15:25, 30 March 2016 (UTC)
::::There is also the question of whether it is fair to lump multiple species of ants or beetles together when determining "most individuals" or "largest biomass". Even the "individual" bit is somewhat ambiguous. Is the "largest organism" listed at [[Clonal colony#Record colonies]] one individual or thousands? Is a [[Volvox]] one individual or many? See [[Slime mold#Behavior]] for a colony that is "no more than a bag of amoebae encased in a thin slime sheath, yet they manage to have various behaviours that are equal to those of animals who possess muscles and nerves with ganglia – that is, simple brains." Also see: [[Largest organisms]]. --[[User:Guy Macon|Guy Macon]] ([[User talk:Guy Macon|talk]]) 15:46, 30 March 2016 (UTC)
:::::Even, to add to the excellent points you are making, the [[species problem]].  --[[User:Jayron32|<span style="color:#009">Jayron</span>]][[User talk:Jayron32|<b style="color:#090">''32''</b>]] 18:41, 30 March 2016 (UTC)
:Note that bacteria aren't animals, so even if they are more numerous, they wouldn't count for the original stat. [[User:Wardog|Iapetus]] ([[User talk:Wardog|talk]]) 16:12, 31 March 2016 (UTC)