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Changed:
to:
to correctly account for the initial angular displacement — Preceding unsigned comment added by 173.180.188.238 ( talk • contribs) 06:05, 20 November 2010 (UTC)
I wonder if it's very correct to say that , or (u+v)/2, even if the time difference is assumed to be very small... that's probably why I never have encountered those equations, at school or at the university... Might be useful though for physics programming, for example. —The preceding unsigned comment was added by 82.181.203.54 ( talk) 12:01, August 21, 2007 (UTC)
Can anyone remember how those 4 equations are derived (presumably, from Newton's Laws)? -- Tarquin 05:19, 30 July 2002 (UTC)
Hey, maybe It's different in Australia (though I cannot understand why), but I have always been taught that displacement is represented by x, and s represents speed (as distinct from velocity, speed is distance traveled over time, velocity is displacement over time and is a vector) Just a thought. — Preceding unsigned comment added by 202.45.119.135 ( talk • contribs) 22:58, 19 November 2007 (UTC)
Is anyone else bothered by the fact that at least 3 different notations are used in this article, e.g. d = distance = s; initialocity = u = v0 = vi; etc. etc.
Also, why 'current'? These equations work perfectly well if the 'final velocity' is not current. Ian Cairns 16:48, 13 Oct 2004 (UTC)
Just adding here that the average velocity is not the half the final velocity, but rather half the initial velocity minus the final velocity. I added this in to the article. - Aldo — Preceding unsigned comment added by 2001:1388:803:9D53:CC95:8D5:857A:FBE1 ( talk) 06:16, 26 September 2014 (UTC)
Thinking it may be worthwhile changing everything into SUVAT, and adding a note at the start that Vf=V, Vi=U, etc. Basically, mentioning that there's other notations used, but in this article, the notion used will be SUVAT. Anyone agrees? -Aldo — Preceding unsigned comment added by 2001:1388:803:9D53:E0C6:BB2B:E975:4285 ( talk) 21:54, 26 September 2014 (UTC)
What happened to s = vt - ½at²? ThomasWinwood 19:08, May 11, 2005 (UTC)
Torricelli's Equation Should this be merged and redirected? Atomiktoaster 00:32, 10 Jun 2005 (UTC)
Hi, I would like to suggest some corrections in this article. There are many examples of equation of motions, but in fact there is only one equation of motion for mechanical systems,
where, m is the system mass and a is the acceleration. Thank you.
Paulo — Preceding unsigned comment added by Paupitz ( talk • contribs) 10:09, 19 February 2007 (UTC)
My science teacher told me that they changed the pronumeral for displacement from "s" to "R". Is this OK? The Updater would like to talk to you! 07:48, 22 March 2007 (UTC)
I was taught it was x, and s was for speed (distance over time NOT velicty which is displacement over time). R is resistance isn't it...? don't motion formulea only use lower case? —Preceding unsigned comment added by 202.45.119.135 ( talk) 23:02, 19 November 2007 (UTC)
Notation is abused all the time, however, "r" is the radial distance in polar co-ordinates, "x" is one of the components (the others usually "y" and "z") in cartesian co-ordinates and "s" is something high school teachers come up with for displacement as they've already used "d" for distance. "R" is almost always resistance. At any rate it really doesn't matter as long as it's clearly labeled. Durinix ( talk) 13:32, 2 April 2008 (UTC)
You can call it what ever you like. Different text books use different symbols. "s" is the most common for displacement in physics, in engineering it could be "d", "s" or whatever random variable you have in your free body diagram for example. —Preceding unsigned comment added by 66.134.78.115 ( talk) 18:02, 22 July 2008 (UTC)
Why is this article called "Equation of motion" when it is clearly about more than a single equation? Even the opening sentence says "equations of motion". -- Dr Greg ( talk) 13:15, 4 March 2008 (UTC)
The correct equations are given with proper derivation at User:Narendra_Sisodiya/mechanics
Equation give on the page are not correct as
If you're going to do a complete redirection of this article to another one, then it would be better to have some discussion on the talk page as well as the edit summary. I propose that this information stay. It is useful, although technically it is covered elsewhere, without providing the simplified classical statememnts of the equations of motion I think that something is lost in removing this article. I would be happy for a redirect if the final pages ended up having this content in them (without the requirement for readers to understand calculus). Angelamaher ( talk) 10:20, 19 September 2008 (UTC)
or
- Sanpaz ( talk) 15:41, 19 September 2008 (UTC)
I notice an IP's inconsistently replaced "s" with "x" in some of the equations and descriptions. I'm reverting that. My reasoning is:
Some equations for the motion of charged particles shold be inserted.-- 86.126.25.12 ( talk) 18:33, 29 August 2011 (UTC)
I think the current definition of "Equations of motion": "Equations of motion are equations that describe the behavior of a system as a function of time.", is too broad, too vague. The heat equation describes the behavior of a system in which heat flow occurs as a function of time, but it isn't an equation of motion. I don't have an alternative formulation at this point, just wanted to see if people would agree with me. /Andreas — Preceding unsigned comment added by Andreasdr ( talk • contribs) 09:39, 6 October 2011 (UTC)
The derivations should be updated as they are too brief and need to be more intuitive, the derivations on the [Velocity] page (in the equations of motion section) are much better and easier to follow. "Shine on you crazy diamond" ( talk) 14:33, 11 December 2011 (UTC)
This article appears to present the equations of motion of a single body in a uniform gravitational field, or perhaps in no gravitational field at all. Yet the title does not imply such a limitation. I see no equations that describe the motions of two bodies in mutual gravitational attraction, and no discussion of the difficulty (perhaps the impossibility) of constructing closed-form equations for systems containing three or more bodies (the Three-body problem). Something needs changing. David Spector (talk) 20:54, 29 December 2011 (UTC)
The recent rewrite of this article goes too far imho. The previous version concentrated on the classic equations of motion which, for most people, is what they are seeking in this article. If it is felt there is a need for mention of these more esoteric areas then surely this could be achieved better by pointing to other suitable articles rather than swamping this article and potentially confusing the reader simply seeking information on the "equations of motion". Abtract ( talk) 22:47, 30 December 2011 (UTC)
Here is my intended structure. In each case everything will be very briefly stated, and plenty of links will be included.
Newtonian mechanics
Kinematics: translations and rotations of one particle
Kinematics: vibrations of one particle
Dynamics: translations and rotations of one particle
Dynamics of many particles
Lagrangian + Hamiltonian mechanics
Electrodynamics
Relativitistic motion? (again this will mostly point to other articles)
(Very briefly) Wave motion (this section will mostly be a couple of paragraphs, pointing to the main articles)
Also i'll modify the see also section. -- F = q( E + v × B) 12:45, 2 January 2012 (UTC)
Great edit, but please note that given [1]-[2] in the section constant linear acceleration:
The equation of average velocity can be derived as:
That said average velocity is redundant in the derivation. Please refer to other text besides the one cited if this is not clear. Also, spatial information is lost if you take the magnitude, since bold r is a vector and r is just a scalar. hoo0 ( talk) 02:10, 14 January 2012 (UTC) Actually, please just refer to Kinematics#Kinematics_of_constant_acceleration, the better way to express this. hoo0 ( talk) 03:40, 14 January 2012 (UTC)
Please consider the general definition below:
Note that by this definition, differential equations are not by default Equations of motion, only their solutions describing the motion. This is consistent with the attempts in the article to express motion as functions of time, position, velocity and acceleration. This definition also separates the kinematics nature of the equations from the dynamics of force, momentum and energy. It is also valid in general relativity, as Einstein field equations are differential equations describing gravity with solutions such as the Schwarzschild_metric. hoo0 ( talk) 06:22, 14 January 2012 (UTC)
Given Hamilton's equations:
then Maschen correctly wrote that if you take each equation, switch pi for qi, and H for −H, the equations are the same:
So its not about the antisymmetry of only interchanging pi and qi, he wrote about simaltaneously switching H for −H also. F = q(E+v×B) ⇄ ∑ici 07:29, 31 March 2012 (UTC)
The SUVAT equations do have limited application; they can only be used in classical mechanics since it would be possible to accelerate beyond the speed of light, and even then they only apply for constant acceleration.
The statement as it read:
is correct. Why delete it? And why "relativity is the exception not the norm"? Isn't relativity the extension from classical mechanics to speeds approaching light? Back-reverted. F = q(E+v×B) ⇄ ∑ici 10:22, 3 April 2012 (UTC)
Thank you - I'll revert and apologies for not thinking clearly and behaving stupidly and rudely. =( F = q(E+v×B) ⇄ ∑ici 14:04, 3 April 2012 (UTC)
Some equations (kinematic and dynamic) concerning the motions on spirals should be added.-- 188.26.22.131 ( talk) 14:57, 14 August 2012 (UTC)
Is this necessary?
The section Equations of motion (Quantitative) first mentions the position and momentum vectors, then gives a detailed description in section Equations of motion (Position vector) of the position vector in various coordinate systems. This should be in the main article Position vector.
Same for the generalized coordinates in the section Equations of motion (Generalized coordinates). Much of this could be moved to Analytical mechanics (D'Alembert's principle, generalized coordinates and constraints), because it’s a brief general description, rather than the main article generalized coordinates since links direct to there.
I intend to make these changes now. Maschen ( talk) 10:47, 15 August 2012 (UTC)
I added some information regarding the average velocity for constant acceleration: Arithmetic mean of the final velocity minus the initial velocity.
However, I have no idea how to put this in so it looks like an equation. if someone could help out, it'd be greatly appreciated. -Aldo — Preceding unsigned comment added by 2001:1388:803:9d53:cc95:8d5:857a:fbe1 ( talk) 06:18, September 26, 2014 (UTC)
I actually got the equation wrong, it was the initial PLUS the final, divided by 2.
It is included in the SUVAT equations, but there's no pointing out that it's the equation for average velocity. It's just displacement = (vf-v0)/2 * t, which is the displacement, USING the average velocity. However, before that equation, there's no indication that it's the formula for the average velocity. Perhaps this should be added? What are your thoughts on this? -Aldo — Preceding unsigned comment added by 2001:1388:803:9D53:E0C6:BB2B:E975:4285 ( talk) 21:48, 26 September 2014 (UTC)
Works for me; what about the notation though? As someone mentioned above, the article uses both SUVAT and Vf, Vi, etc... Perhaps we should add a section mentioning that there's many notations in use, and saying that the article will only use one (Personally, I'd go for SUVAT). Maybe that would make it clearer?
At the moment, it seems like a collage of equations (correct equations, obviously) but taken from different sources, which makes the article kind of difficult to follow. Thoughts? -Aldo — Preceding unsigned comment added by 2001:1388:803:9D53:E0C6:BB2B:E975:4285 ( talk) 01:17, 27 September 2014 (UTC)
The entire article has begun with higher mathematics here. The article is not for a lay person. It is highly complex and circumlocutory.
An article for the general readers should have a continuous historical perspective, beginning from say, the equations of motion, such as the SUVAT equations:
Then we move from Galileo to Newton, to Euler, Langrange, and others.
It is believed that no topic is difficult to understand even for a lay person if laid out logically, branching out at specific places and again agglomerated to a common basis. Complexity would make an article appear as highly technical but would lose readers. The entire article has to be re-written considering and citing exact historical dates/era/epochs.
Otherwise, this is going to do more harm to Wikipedia and general public than good.
Bkpsusmitaa ( talk) 06:20, 11 August 2015 (UTC)
I have tried my best to cover the arrival of a primitive form of SUVAT equation. But I have to dig deep within literature to find out the beginning of the usage of the modern SUVAT formulae. Reading, reading, ... Bkpsusmitaa ( talk) 07:07, 19 August 2015 (UTC)
I beleive you have a sign wrong in your Hamiltonian (electrodynamics), It is supposed to be :
since
It would probably be useful to mention that for simple systems the Lagrangian is the kinetic energy MINUS the potential energy and the Hamiltonian the kinetic energy PLUS the potential energy. Also the so called ACTION integral earlier in the article is a path integral, over the path that make the action stationary, OR I think just don't go into these details. Regarding the other parts of the article, may I suggest to make it clear that r in Cartesian coordinates is r = (x,y,z) and show how the equations then get split up in one per coordinate. Everybody seems to think that it is obvious that there are no interaction between coordinates and of course the vector nature of the equations indicate that but, it is a kind of miracle that it is true so should be pointed out. SUVAT must be some kind of American thing. Never heard about it, and things like that does not seem to encourage any kind of thinking. To be honest I liked your article a lot for its good historical introduction and the initial equations, but less and less reading along. Too much to be a simple introductory article. [[ Burningbrand ( talk) 09:56, 30 August 2015 (UTC)]]
The comment(s) below were originally left at Talk:Equations of motion/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
Comment(s) | Press [show] to view → |
---|---|
Spacetime is not a fundamental entity.
Time and space are like the x,y, cartesan coordinate axes to help locating "events". An 'event' could be defined as the smallest unit of "change" ( measurable or not), occuring in the inter or intra relationships between energy states ( radiating or massive or dark , in cosmic vacuum).Energy is always in an ever-vibrational mode. Change is the defining quality of energy. Like Lee-simolin said , spacetime doesnt exist independent of events. Spacetime is a relational parameter and not absolute parameters.An example given ( an example which goes a long way though not all the way ), is that spacetime is just like a sentencein any written form of communication, in which the words are likened to events. This makes spacetime as an emergent phenomena and events ( changes with respect to other changes) as the more fundamental phenomena. Spacetime is the hardware and change is the operating software.Phenomena is a network of changes ( or exchanges).A computer is NOT a computer without its operational software.To discern changes we created the artifact of spacetime. Change with respect to what ? Not with respect to space or time or spacetime, rather it is Change with respect to other events ie, other configurations of change in relationships . Spacetime is a mathematical artifact ( artificial reference boundaries),like the definition of the cartesan coordinate system to make it easy to grasp and fix 'changes in the relationships' that keep coursing through the universe to some degree of perpetuity in our minds (at least giving changes some sort of instataneous 'stability', like we freeze-study static electricity ),and make it manipulatively comprehensible to our senses. Changes apparently occur continuously, at macrocosmic scales but actually fluctuating discretly at nanocosmic ranges. Macrocosm is but a statistically averaged stable state or condition of the randomly chaotic microcosm .Like our integers which are but averaged states of infinite fluctuations at specific nodes, pre-specified just to suit our convenience , arbitarily. Spacetime is just like a net to catch events, to take it home. And, what is a net? In Johnson's english dictionary,( the very first english dictionary ever published ) it is succintly defined as "holes tied together" .Events are "nothingness' tied together.Spacetime is derived out of events.Events give meaning to spacetime.Spacetime is also one of the catches of events. There are events that transcend spacetime like the null event, or the non-causal spontaneous vacuum fluctuations in quantum science.For events to occur ( ie,relatinships to change )spacetime is not a pre-requisite. But for spacetime to be born 'events' are a must. 'Spacetime is the language in which changes in relationships are expressed .'. one of the languages of spacetime is mathematics. Other languages to express spacetime in a manner that is appealing to our senses,may be fine art or the universe of sound,or through 'feelings' of the mind. This provides an 'exchange rate' to 'feelings' with mathematical logic for the expression of changes,manifest or unmanifest. Further discussions are welcome . < theunnies at yahoo.com > theunnies |
Last edited at 19:19, 8 June 2008 (UTC). Substituted at 14:34, 29 April 2016 (UTC)
The article asserts "Galileo deduced the equation s = 1/2gt2 in his work geometrically,[4] using the Merton rule, now known as a special case of one of the equations of kinematics". This is simply not true. Nowhere in Galileo's work can one find something like that. Galileo's true law of free fall reads v ~ t, thsat is, v:t = constant. Generally Galileo does not use equations (structure A = A) but geometric proportions (structure A:B = C:D = k = constant). Ed Dellian. 2003:D2:9722:6B80:18F3:7E61:E1C9:E584 ( talk) 12:30, 29 September 2020 (UTC)
This
level-4 vital article is rated B-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||||||||||||
|
Changed:
to:
to correctly account for the initial angular displacement — Preceding unsigned comment added by 173.180.188.238 ( talk • contribs) 06:05, 20 November 2010 (UTC)
I wonder if it's very correct to say that , or (u+v)/2, even if the time difference is assumed to be very small... that's probably why I never have encountered those equations, at school or at the university... Might be useful though for physics programming, for example. —The preceding unsigned comment was added by 82.181.203.54 ( talk) 12:01, August 21, 2007 (UTC)
Can anyone remember how those 4 equations are derived (presumably, from Newton's Laws)? -- Tarquin 05:19, 30 July 2002 (UTC)
Hey, maybe It's different in Australia (though I cannot understand why), but I have always been taught that displacement is represented by x, and s represents speed (as distinct from velocity, speed is distance traveled over time, velocity is displacement over time and is a vector) Just a thought. — Preceding unsigned comment added by 202.45.119.135 ( talk • contribs) 22:58, 19 November 2007 (UTC)
Is anyone else bothered by the fact that at least 3 different notations are used in this article, e.g. d = distance = s; initialocity = u = v0 = vi; etc. etc.
Also, why 'current'? These equations work perfectly well if the 'final velocity' is not current. Ian Cairns 16:48, 13 Oct 2004 (UTC)
Just adding here that the average velocity is not the half the final velocity, but rather half the initial velocity minus the final velocity. I added this in to the article. - Aldo — Preceding unsigned comment added by 2001:1388:803:9D53:CC95:8D5:857A:FBE1 ( talk) 06:16, 26 September 2014 (UTC)
Thinking it may be worthwhile changing everything into SUVAT, and adding a note at the start that Vf=V, Vi=U, etc. Basically, mentioning that there's other notations used, but in this article, the notion used will be SUVAT. Anyone agrees? -Aldo — Preceding unsigned comment added by 2001:1388:803:9D53:E0C6:BB2B:E975:4285 ( talk) 21:54, 26 September 2014 (UTC)
What happened to s = vt - ½at²? ThomasWinwood 19:08, May 11, 2005 (UTC)
Torricelli's Equation Should this be merged and redirected? Atomiktoaster 00:32, 10 Jun 2005 (UTC)
Hi, I would like to suggest some corrections in this article. There are many examples of equation of motions, but in fact there is only one equation of motion for mechanical systems,
where, m is the system mass and a is the acceleration. Thank you.
Paulo — Preceding unsigned comment added by Paupitz ( talk • contribs) 10:09, 19 February 2007 (UTC)
My science teacher told me that they changed the pronumeral for displacement from "s" to "R". Is this OK? The Updater would like to talk to you! 07:48, 22 March 2007 (UTC)
I was taught it was x, and s was for speed (distance over time NOT velicty which is displacement over time). R is resistance isn't it...? don't motion formulea only use lower case? —Preceding unsigned comment added by 202.45.119.135 ( talk) 23:02, 19 November 2007 (UTC)
Notation is abused all the time, however, "r" is the radial distance in polar co-ordinates, "x" is one of the components (the others usually "y" and "z") in cartesian co-ordinates and "s" is something high school teachers come up with for displacement as they've already used "d" for distance. "R" is almost always resistance. At any rate it really doesn't matter as long as it's clearly labeled. Durinix ( talk) 13:32, 2 April 2008 (UTC)
You can call it what ever you like. Different text books use different symbols. "s" is the most common for displacement in physics, in engineering it could be "d", "s" or whatever random variable you have in your free body diagram for example. —Preceding unsigned comment added by 66.134.78.115 ( talk) 18:02, 22 July 2008 (UTC)
Why is this article called "Equation of motion" when it is clearly about more than a single equation? Even the opening sentence says "equations of motion". -- Dr Greg ( talk) 13:15, 4 March 2008 (UTC)
The correct equations are given with proper derivation at User:Narendra_Sisodiya/mechanics
Equation give on the page are not correct as
If you're going to do a complete redirection of this article to another one, then it would be better to have some discussion on the talk page as well as the edit summary. I propose that this information stay. It is useful, although technically it is covered elsewhere, without providing the simplified classical statememnts of the equations of motion I think that something is lost in removing this article. I would be happy for a redirect if the final pages ended up having this content in them (without the requirement for readers to understand calculus). Angelamaher ( talk) 10:20, 19 September 2008 (UTC)
or
- Sanpaz ( talk) 15:41, 19 September 2008 (UTC)
I notice an IP's inconsistently replaced "s" with "x" in some of the equations and descriptions. I'm reverting that. My reasoning is:
Some equations for the motion of charged particles shold be inserted.-- 86.126.25.12 ( talk) 18:33, 29 August 2011 (UTC)
I think the current definition of "Equations of motion": "Equations of motion are equations that describe the behavior of a system as a function of time.", is too broad, too vague. The heat equation describes the behavior of a system in which heat flow occurs as a function of time, but it isn't an equation of motion. I don't have an alternative formulation at this point, just wanted to see if people would agree with me. /Andreas — Preceding unsigned comment added by Andreasdr ( talk • contribs) 09:39, 6 October 2011 (UTC)
The derivations should be updated as they are too brief and need to be more intuitive, the derivations on the [Velocity] page (in the equations of motion section) are much better and easier to follow. "Shine on you crazy diamond" ( talk) 14:33, 11 December 2011 (UTC)
This article appears to present the equations of motion of a single body in a uniform gravitational field, or perhaps in no gravitational field at all. Yet the title does not imply such a limitation. I see no equations that describe the motions of two bodies in mutual gravitational attraction, and no discussion of the difficulty (perhaps the impossibility) of constructing closed-form equations for systems containing three or more bodies (the Three-body problem). Something needs changing. David Spector (talk) 20:54, 29 December 2011 (UTC)
The recent rewrite of this article goes too far imho. The previous version concentrated on the classic equations of motion which, for most people, is what they are seeking in this article. If it is felt there is a need for mention of these more esoteric areas then surely this could be achieved better by pointing to other suitable articles rather than swamping this article and potentially confusing the reader simply seeking information on the "equations of motion". Abtract ( talk) 22:47, 30 December 2011 (UTC)
Here is my intended structure. In each case everything will be very briefly stated, and plenty of links will be included.
Newtonian mechanics
Kinematics: translations and rotations of one particle
Kinematics: vibrations of one particle
Dynamics: translations and rotations of one particle
Dynamics of many particles
Lagrangian + Hamiltonian mechanics
Electrodynamics
Relativitistic motion? (again this will mostly point to other articles)
(Very briefly) Wave motion (this section will mostly be a couple of paragraphs, pointing to the main articles)
Also i'll modify the see also section. -- F = q( E + v × B) 12:45, 2 January 2012 (UTC)
Great edit, but please note that given [1]-[2] in the section constant linear acceleration:
The equation of average velocity can be derived as:
That said average velocity is redundant in the derivation. Please refer to other text besides the one cited if this is not clear. Also, spatial information is lost if you take the magnitude, since bold r is a vector and r is just a scalar. hoo0 ( talk) 02:10, 14 January 2012 (UTC) Actually, please just refer to Kinematics#Kinematics_of_constant_acceleration, the better way to express this. hoo0 ( talk) 03:40, 14 January 2012 (UTC)
Please consider the general definition below:
Note that by this definition, differential equations are not by default Equations of motion, only their solutions describing the motion. This is consistent with the attempts in the article to express motion as functions of time, position, velocity and acceleration. This definition also separates the kinematics nature of the equations from the dynamics of force, momentum and energy. It is also valid in general relativity, as Einstein field equations are differential equations describing gravity with solutions such as the Schwarzschild_metric. hoo0 ( talk) 06:22, 14 January 2012 (UTC)
Given Hamilton's equations:
then Maschen correctly wrote that if you take each equation, switch pi for qi, and H for −H, the equations are the same:
So its not about the antisymmetry of only interchanging pi and qi, he wrote about simaltaneously switching H for −H also. F = q(E+v×B) ⇄ ∑ici 07:29, 31 March 2012 (UTC)
The SUVAT equations do have limited application; they can only be used in classical mechanics since it would be possible to accelerate beyond the speed of light, and even then they only apply for constant acceleration.
The statement as it read:
is correct. Why delete it? And why "relativity is the exception not the norm"? Isn't relativity the extension from classical mechanics to speeds approaching light? Back-reverted. F = q(E+v×B) ⇄ ∑ici 10:22, 3 April 2012 (UTC)
Thank you - I'll revert and apologies for not thinking clearly and behaving stupidly and rudely. =( F = q(E+v×B) ⇄ ∑ici 14:04, 3 April 2012 (UTC)
Some equations (kinematic and dynamic) concerning the motions on spirals should be added.-- 188.26.22.131 ( talk) 14:57, 14 August 2012 (UTC)
Is this necessary?
The section Equations of motion (Quantitative) first mentions the position and momentum vectors, then gives a detailed description in section Equations of motion (Position vector) of the position vector in various coordinate systems. This should be in the main article Position vector.
Same for the generalized coordinates in the section Equations of motion (Generalized coordinates). Much of this could be moved to Analytical mechanics (D'Alembert's principle, generalized coordinates and constraints), because it’s a brief general description, rather than the main article generalized coordinates since links direct to there.
I intend to make these changes now. Maschen ( talk) 10:47, 15 August 2012 (UTC)
I added some information regarding the average velocity for constant acceleration: Arithmetic mean of the final velocity minus the initial velocity.
However, I have no idea how to put this in so it looks like an equation. if someone could help out, it'd be greatly appreciated. -Aldo — Preceding unsigned comment added by 2001:1388:803:9d53:cc95:8d5:857a:fbe1 ( talk) 06:18, September 26, 2014 (UTC)
I actually got the equation wrong, it was the initial PLUS the final, divided by 2.
It is included in the SUVAT equations, but there's no pointing out that it's the equation for average velocity. It's just displacement = (vf-v0)/2 * t, which is the displacement, USING the average velocity. However, before that equation, there's no indication that it's the formula for the average velocity. Perhaps this should be added? What are your thoughts on this? -Aldo — Preceding unsigned comment added by 2001:1388:803:9D53:E0C6:BB2B:E975:4285 ( talk) 21:48, 26 September 2014 (UTC)
Works for me; what about the notation though? As someone mentioned above, the article uses both SUVAT and Vf, Vi, etc... Perhaps we should add a section mentioning that there's many notations in use, and saying that the article will only use one (Personally, I'd go for SUVAT). Maybe that would make it clearer?
At the moment, it seems like a collage of equations (correct equations, obviously) but taken from different sources, which makes the article kind of difficult to follow. Thoughts? -Aldo — Preceding unsigned comment added by 2001:1388:803:9D53:E0C6:BB2B:E975:4285 ( talk) 01:17, 27 September 2014 (UTC)
The entire article has begun with higher mathematics here. The article is not for a lay person. It is highly complex and circumlocutory.
An article for the general readers should have a continuous historical perspective, beginning from say, the equations of motion, such as the SUVAT equations:
Then we move from Galileo to Newton, to Euler, Langrange, and others.
It is believed that no topic is difficult to understand even for a lay person if laid out logically, branching out at specific places and again agglomerated to a common basis. Complexity would make an article appear as highly technical but would lose readers. The entire article has to be re-written considering and citing exact historical dates/era/epochs.
Otherwise, this is going to do more harm to Wikipedia and general public than good.
Bkpsusmitaa ( talk) 06:20, 11 August 2015 (UTC)
I have tried my best to cover the arrival of a primitive form of SUVAT equation. But I have to dig deep within literature to find out the beginning of the usage of the modern SUVAT formulae. Reading, reading, ... Bkpsusmitaa ( talk) 07:07, 19 August 2015 (UTC)
I beleive you have a sign wrong in your Hamiltonian (electrodynamics), It is supposed to be :
since
It would probably be useful to mention that for simple systems the Lagrangian is the kinetic energy MINUS the potential energy and the Hamiltonian the kinetic energy PLUS the potential energy. Also the so called ACTION integral earlier in the article is a path integral, over the path that make the action stationary, OR I think just don't go into these details. Regarding the other parts of the article, may I suggest to make it clear that r in Cartesian coordinates is r = (x,y,z) and show how the equations then get split up in one per coordinate. Everybody seems to think that it is obvious that there are no interaction between coordinates and of course the vector nature of the equations indicate that but, it is a kind of miracle that it is true so should be pointed out. SUVAT must be some kind of American thing. Never heard about it, and things like that does not seem to encourage any kind of thinking. To be honest I liked your article a lot for its good historical introduction and the initial equations, but less and less reading along. Too much to be a simple introductory article. [[ Burningbrand ( talk) 09:56, 30 August 2015 (UTC)]]
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Spacetime is not a fundamental entity.
Time and space are like the x,y, cartesan coordinate axes to help locating "events". An 'event' could be defined as the smallest unit of "change" ( measurable or not), occuring in the inter or intra relationships between energy states ( radiating or massive or dark , in cosmic vacuum).Energy is always in an ever-vibrational mode. Change is the defining quality of energy. Like Lee-simolin said , spacetime doesnt exist independent of events. Spacetime is a relational parameter and not absolute parameters.An example given ( an example which goes a long way though not all the way ), is that spacetime is just like a sentencein any written form of communication, in which the words are likened to events. This makes spacetime as an emergent phenomena and events ( changes with respect to other changes) as the more fundamental phenomena. Spacetime is the hardware and change is the operating software.Phenomena is a network of changes ( or exchanges).A computer is NOT a computer without its operational software.To discern changes we created the artifact of spacetime. Change with respect to what ? Not with respect to space or time or spacetime, rather it is Change with respect to other events ie, other configurations of change in relationships . Spacetime is a mathematical artifact ( artificial reference boundaries),like the definition of the cartesan coordinate system to make it easy to grasp and fix 'changes in the relationships' that keep coursing through the universe to some degree of perpetuity in our minds (at least giving changes some sort of instataneous 'stability', like we freeze-study static electricity ),and make it manipulatively comprehensible to our senses. Changes apparently occur continuously, at macrocosmic scales but actually fluctuating discretly at nanocosmic ranges. Macrocosm is but a statistically averaged stable state or condition of the randomly chaotic microcosm .Like our integers which are but averaged states of infinite fluctuations at specific nodes, pre-specified just to suit our convenience , arbitarily. Spacetime is just like a net to catch events, to take it home. And, what is a net? In Johnson's english dictionary,( the very first english dictionary ever published ) it is succintly defined as "holes tied together" .Events are "nothingness' tied together.Spacetime is derived out of events.Events give meaning to spacetime.Spacetime is also one of the catches of events. There are events that transcend spacetime like the null event, or the non-causal spontaneous vacuum fluctuations in quantum science.For events to occur ( ie,relatinships to change )spacetime is not a pre-requisite. But for spacetime to be born 'events' are a must. 'Spacetime is the language in which changes in relationships are expressed .'. one of the languages of spacetime is mathematics. Other languages to express spacetime in a manner that is appealing to our senses,may be fine art or the universe of sound,or through 'feelings' of the mind. This provides an 'exchange rate' to 'feelings' with mathematical logic for the expression of changes,manifest or unmanifest. Further discussions are welcome . < theunnies at yahoo.com > theunnies |
Last edited at 19:19, 8 June 2008 (UTC). Substituted at 14:34, 29 April 2016 (UTC)
The article asserts "Galileo deduced the equation s = 1/2gt2 in his work geometrically,[4] using the Merton rule, now known as a special case of one of the equations of kinematics". This is simply not true. Nowhere in Galileo's work can one find something like that. Galileo's true law of free fall reads v ~ t, thsat is, v:t = constant. Generally Galileo does not use equations (structure A = A) but geometric proportions (structure A:B = C:D = k = constant). Ed Dellian. 2003:D2:9722:6B80:18F3:7E61:E1C9:E584 ( talk) 12:30, 29 September 2020 (UTC)