<p>There are a <em>lot</em> of instances (such as those you pointed out) in all of science and mathematics where a symbol can mean two different things. <a href="https://en.wikipedia.org/wiki/List_of_mathematical_symbols" rel="nofollow">In mathematics</a>, there's actually a good deal of this (and the article says that the list is incomplete!). Many are <a href="https://en.wikipedia.org/wiki/List_of_mathematical_symbols#Letter-based_symbols" rel="nofollow">based on letters</a>, although they may have deviated from the original shape in order to make a distinction regarding just what the heck the thing actually means.</p>

<p>Eventually, you run out of letters. You can opt to use symbols from <a href="https://en.wikipedia.org/wiki/Greek_letters_used_in_mathematics,_science,_and_engineering" rel="nofollow">another language</a>, the first choice for many being Greek. That roughly doubles the amount of letter-based symbols available to you. But there are still a lot of duplicates, as you can see by browsing through the lists <a href="https://en.wikipedia.org/wiki/Physical_constant" rel="nofollow">here</a> and <a href="https://en.wikipedia.org/wiki/List_of_common_physics_notations" rel="nofollow">here</a>.</p>

<p>To my knowledge, this is the most comprehensive list easily available. And yes, there are loads of duplicates. But the great thing is that you almost certainly won't have to use the same variable to mean multiple things in one equation, or set of equations. For example, I doubt you'll need to use $V$ for voltage, volume and shear force all in the same equation!</p>

CC BY-SA 3.0
2014-10-23T22:59:05.740Z
Very helpful, thanks.  Already found 2 more symbols for angular momentum!
steveOw
CC BY-SA 3.0
2014-10-23T23:02:50.143Z
@steveOw I meant to clarify, not confuse! But seriously, a wider range of symbols means you can make equations a lot more clearer.
HDE 226868
CC BY-SA 3.0
2014-10-23T23:12:33.537Z
I guess that is an upside but I wish in this digital age that we could just invent new symbols to avoid multiple use.  I'm finding it hard sometimes to learn new concepts when referring to different articles using different notations. In one textbook the author even uses the same symbol for different things, without flagging which meaning he intends!
steveOw
CC BY-SA 3.0
2014-10-23T23:17:22.600Z
I feel your pain. Nothing like poor usage of symbols to make a confusing idea even more confusing. Or a simple idea confusing.
HDE 226868
CC BY-SA 3.0
2014-10-24T00:18:07.707Z
I give you the radial component of the electron wavefunction for the ground state of hydrogen (in units of $4\pi\epsilon_0=1$):
$$\psi(r) = \frac{m^{3/2} e^3}{\pi^{1/2} \hbar^3}\,e^{-m e^2 r/\hbar^2}\text{.}$$
Notably, $e$ plays a dual role even in the same equation (Euler's constant or fundamental charge). If I were evil, I'd also play with $\pi$ used for the transcendental number and conjugate momentum at once.
Stan Liou
CC BY-SA 3.0
2014-10-24T00:26:10.410Z
@StanLiou Curses. At least I put "almost". . . By the way, where did you get that equation? It looks interesting.
HDE 226868
CC BY-SA 3.0
2014-10-24T00:44:00.023Z
@HDE226868 From any introductory quantum mechanics textbook, the radial part of the ground state is $2a_0^{-3/2}e^{-r/a_0}$, where $a_0 = 4\pi\epsilon_0\hbar^2/me^2$ is the Bohr radius; use of units of $4\pi\epsilon_0=1$ is a simplification. However, I confess that I've never seen it written out all at once with the Bohr radius substituted in **and** $e$ (as opposed to $\exp$) for the exponential, except as an illustration of just this point of overloading letters. (This particular use, IIRC, is from *The Tau Manifesto*.)
Stan Liou
CC BY-SA 3.0
2014-10-24T10:33:25.123Z
@StanLiou, The correct form of the wavefunction should be: $\psi(r) = \frac{m^{3/2}e^3}{\pi^{1/2}\hbar^3}\textrm{e}^{-me^2r/\hbar^2}$. Please note the fact that the exponent is written in non-italic form, while Euler's constant is italic. Physical quantities (and constants) should be printed in italics while units and math constants should be printed 'straight'. So there should not be any ambiguity here if the author conforms to the standards.
Dieudonné
CC BY-SA 3.0
2014-10-24T11:46:00.807Z
@Dieudonné That might be a good practice to adopt, but whose standard is it? I honestly can't recall even seeing even a single physics author uses a Roman-face $\mathrm{e}$ for Euler's constant. Out of sheer boredom, I've double-checked a few of the books in my immediate vicinity that had reasons to discuss electrons--ones by D.Griffiths (QM), J.J.Sakurai (QM), R.Shankar (QM), A.Zee (QFT), J.Polchinski (ST), J.D.Jackson (EM)--and every single one of them had an unremarkable $e$ for Euler's constant.
Stan Liou
CC BY-SA 3.0
2014-10-24T12:08:22.747Z
@StanLiou No, the exponent ($\exp$) should be written in roman form, not Euler's constant. The fundamental charge is often used as a unit. Maybe the word 'standard' was not the correct word. The conventions are from the International System of Units and can for instance be found at http://physics.nist.gov/cuu/Units/checklist.html
Dieudonné
CC BY-SA 3.0
2014-10-24T12:11:19.447Z
@StanLiou I guess it is not much of a standard if not many people know of it ;-) Although I would note that for instance LaTeX doe try to conform to the standard when using functions as when using $\log$ (`\log`) instead of $log$ (`log`).
Dieudonné
CC BY-SA 3.0
2014-10-24T12:17:28.847Z
@StanLiou It actually does seem to be a standard: ISO/IEC 80000 - http://en.wikipedia.org/wiki/ISO/IEC_80000.
Dieudonné
CC BY-SA 3.0
2014-10-24T12:17:47.300Z
@Dieudonné Everyone used Roman-faced $\exp$, yes, but I don't see one prescribing $\mathrm{e}^\ldots$ rather than $e^\ldots$ when used Euler's number is referred to directly? Hmm..
Stan Liou
CC BY-SA 3.0
2014-10-24T12:22:24.437Z
@StanLiou Just realised that Euler's constant is the exponent - stupid of me :(. I mixed things up, Euler's constant should be written in italics, the electron charge (as a unit) using Roman face...
Dieudonné
CC BY-SA 3.0
2014-10-23T21:55:28.887Z
2014-10-23T21:55:28.887Z
HDE 226868
<p>There is no formal set of symbols for physical quantities that is recognised by all scientists. Units on the other hand are more formally recognised, e.g. <a href="http://www.bipm.org/en/measurement-units/" rel="nofollow noreferrer">International System of Units</a>. Authors may select their own symbols to denote specific quantities (they should, however, always specify the meaning of a symbol). On the other hand, I imagine that it will be more difficult to get your paper published if you use different symbols then generally used ones.</p>

<p>This problem is a problem of disambiguation and is not limited to the physical sciences. In computer science, the W3C (Tim Berners Lee) has initiated the <a href="http://www.w3.org/standards/semanticweb/" rel="nofollow noreferrer">semantic web</a>, where concepts on the web are tagged with unique identifiers (URIs). Ontologies (vocabularies of concepts) are used to link concepts to URIs, which can be reused for disambiguation. For instance a paper may use symbol <a href="http://www.wurvoc.org/vocabularies/om-1.8/Angular_momentum" rel="nofollow noreferrer">$L$</a> for angular momentum and is linked to a URI for the concept <code>angular momentum</code>. A website may use the symbol <a href="http://www.wurvoc.org/vocabularies/om-1.8/Angular_momentum" rel="nofollow noreferrer">$H$</a> for angular momentum and link to the same concept <code>angular momentum</code> using the same URI. As both symbols are linked to the same concept, they are both disambiguated.</p>

<p>I've been working together with Hajo Rijgersberg (<a href="https://www.cs.vu.nl/en/Images/H%20Rijgersberg%2021mei2013_tcm75-342356.pdf" rel="nofollow noreferrer">see his PhD thesis</a>) on the <a href="http://www.wurvoc.org/vocabularies/om-1.8/" rel="nofollow noreferrer">Ontology of Units of Measure</a>, which is an ontology with a large number of quantities and units.
<strong>This ontology can be used as a list of quantities and their symbols.</strong> But it is by no means complete.</p>

<p>One way we could use such an ontology is to insert the identifier (URI) into the text. At the <a href="http://swaie2014.wordpress.com" rel="nofollow noreferrer">SWAIE workshop</a>, I outlined a method to do just that in LaTeX (<a href="http://ceur-ws.org/Vol-925/paper_5.pdf" rel="nofollow noreferrer">paper</a>). The physical symbols in the PDF output are then linked to the concept. Clicking on the symbol will cause a browser to open at the URL identifying the physical concept. At the moment I'm trying to implement this in MathJax, but I am finding some <a href="https://stackoverflow.com/questions/24514895/how-to-keep-rdfa-attributes-in-mathml-using-mathjax?noredirect=1#comment41599340_24514895">technical difficulties</a>.</p>

CC BY-SA 3.0
2014-10-24T10:18:14.100Z
@Dieudonne.Thanks. It certainly would be useful sometimes to be able to link from a symbol to a concept URI.  It is surprising to me how many texts do not even include a list of symbols used.
steveOw
CC BY-SA 3.0
2014-10-24T09:34:56.907Z
2014-10-24T10:38:08.690Z
2017-05-23T12:37:21.700Z
Dieudonné
<p>Is there a standard mapping of symbols to terms for celestial and orbital mechanics (and physics in general)?</p>

<p>For example here are some ambiguities</p>

<p>Angular Momentum: L, H, J, $\Gamma$,</p>

<p>Orbital period: T or P,</p>

<p>M: mean anomaly or mass of the Sun,</p>

<p>E: energy or eccentric anomaly,</p>

<p>p: linear momentum or length of semi-latus rectum,</p>

<p>a: acceleration or length of semi-major axis,</p>

<p>e: eccentricity or base of natural logarithms,</p>

<orbit><orbital-elements>
Is there a standard mapping of symbols to terms for celestial and orbital mechanics
steveOw
# Is there a standard mapping of symbols to terms for celestial and orbital mechanics

(Asked by: username_0 on 2014-10-23)

Is there a standard mapping of symbols to terms for celestial and orbital mechanics (and physics in general)?

For example here are some ambiguities

Angular Momentum: L, H, J, $\Gamma$,

Orbital period: T or P,

M: mean anomaly or mass of the Sun,

E: energy or eccentric anomaly,

p: linear momentum or length of semi-latus rectum,

a: acceleration or length of semi-major axis,

e: eccentricity or base of natural logarithms,

**Tags:** orbit, orbital-elements

---

## 2 answers

### Answer by username_1 on 2014-10-23. Score: 1 | Accepted answer

There are a *lot* of instances (such as those you pointed out) in all of science and mathematics where a symbol can mean two different things. [In mathematics](https://en.wikipedia.org/wiki/List_of_mathematical_symbols), there's actually a good deal of this (and the article says that the list is incomplete!). Many are [based on letters](https://en.wikipedia.org/wiki/List_of_mathematical_symbols#Letter-based_symbols), although they may have deviated from the original shape in order to make a distinction regarding just what the heck the thing actually means.

Eventually, you run out of letters. You can opt to use symbols from [another language](https://en.wikipedia.org/wiki/Greek_letters_used_in_mathematics,_science,_and_engineering), the first choice for many being Greek. That roughly doubles the amount of letter-based symbols available to you. But there are still a lot of duplicates, as you can see by browsing through the lists [here](https://en.wikipedia.org/wiki/Physical_constant) and [here](https://en.wikipedia.org/wiki/List_of_common_physics_notations).

To my knowledge, this is the most comprehensive list easily available. And yes, there are loads of duplicates. But the great thing is that you almost certainly won't have to use the same variable to mean multiple things in one equation, or set of equations. For example, I doubt you'll need to use $V$ for voltage, volume and shear force all in the same equation!

> **Comments:**
> **username_0**: Very helpful, thanks.  Already found 2 more symbols for angular momentum!  
> **username_1**: @steveOw I meant to clarify, not confuse! But seriously, a wider range of symbols means you can make equations a lot more clearer.  
> **username_0**: I guess that is an upside but I wish in this digital age that we could just invent new symbols to avoid multiple use.  I'm finding it hard sometimes to learn new concepts when referring to different articles using different notations. In one textbook the author even uses the same symbol for different things, without flagging which meaning he intends!  
> **username_1**: I feel your pain. Nothing like poor usage of symbols to make a confusing idea even more confusing. Or a simple idea confusing.  
> **username_2**: I give you the radial component of the electron wavefunction for the ground state of hydrogen (in units of $4\pi\epsilon_0=1$): $$\psi(r) = \frac{m^{3/2} e^3}{\pi^{1/2} \hbar^3}\,e^{-m e^2 r/\hbar^2}\text{.}$$ Notably, $e$ plays a dual role even in the same equation (Euler's constant or fundamental charge). If I were evil, I'd also play with $\pi$ used for the transcendental number and conjugate momentum at once.  
> **username_1**: @StanLiou Curses. At least I put "almost". . . By the way, where did you get that equation? It looks interesting.  
> **username_2**: @HDE226868 From any introductory quantum mechanics textbook, the radial part of the ground state is $2a_0^{-3/2}e^{-r/a_0}$, where $a_0 = 4\pi\epsilon_0\hbar^2/me^2$ is the Bohr radius; use of units of $4\pi\epsilon_0=1$ is a simplification. However, I confess that I've never seen it written out all at once with the Bohr radius substituted in **and** $e$ (as opposed to $\exp$) for the exponential, except as an illustration of just this point of overloading letters. (This particular use, IIRC, is from *The Tau Manifesto*.)  
> **username_3**: @StanLiou, The correct form of the wavefunction should be: $\psi(r) = \frac{m^{3/2}e^3}{\pi^{1/2}\hbar^3}\textrm{e}^{-me^2r/\hbar^2}$. Please note the fact that the exponent is written in non-italic form, while Euler's constant is italic. Physical quantities (and constants) should be printed in italics while units and math constants should be printed 'straight'. So there should not be any ambiguity here if the author conforms to the standards.  
> **username_2**: @Dieudonné That might be a good practice to adopt, but whose standard is it? I honestly can't recall even seeing even a single physics author uses a Roman-face $\mathrm{e}$ for Euler's constant. Out of sheer boredom, I've double-checked a few of the books in my immediate vicinity that had reasons to discuss electrons--ones by D.Griffiths (QM), J.J.Sakurai (QM), R.Shankar (QM), A.Zee (QFT), J.Polchinski (ST), J.D.Jackson (EM)--and every single one of them had an unremarkable $e$ for Euler's constant.  
> **username_3**: @StanLiou No, the exponent ($\exp$) should be written in roman form, not Euler's constant. The fundamental charge is often used as a unit. Maybe the word 'standard' was not the correct word. The conventions are from the International System of Units and can for instance be found at http://physics.nist.gov/cuu/Units/checklist.html  
> **username_3**: @StanLiou I guess it is not much of a standard if not many people know of it ;-) Although I would note that for instance LaTeX doe try to conform to the standard when using functions as when using $\log$ (`\log`) instead of $log$ (`log`).  
> **username_3**: @StanLiou It actually does seem to be a standard: ISO/IEC 80000 - http://en.wikipedia.org/wiki/ISO/IEC_80000.  
> **username_2**: @Dieudonné Everyone used Roman-faced $\exp$, yes, but I don't see one prescribing $\mathrm{e}^\ldots$ rather than $e^\ldots$ when used Euler's number is referred to directly? Hmm..  
> **username_3**: @StanLiou Just realised that Euler's constant is the exponent - stupid of me :(. I mixed things up, Euler's constant should be written in italics, the electron charge (as a unit) using Roman face...  

---

### Answer by username_3 on 2014-10-24. Score: 1

There is no formal set of symbols for physical quantities that is recognised by all scientists. Units on the other hand are more formally recognised, e.g. [International System of Units](http://www.bipm.org/en/measurement-units/). Authors may select their own symbols to denote specific quantities (they should, however, always specify the meaning of a symbol). On the other hand, I imagine that it will be more difficult to get your paper published if you use different symbols then generally used ones.

This problem is a problem of disambiguation and is not limited to the physical sciences. In computer science, the W3C (Tim Berners Lee) has initiated the [semantic web](http://www.w3.org/standards/semanticweb/), where concepts on the web are tagged with unique identifiers (URIs). Ontologies (vocabularies of concepts) are used to link concepts to URIs, which can be reused for disambiguation. For instance a paper may use symbol [$L$](http://www.wurvoc.org/vocabularies/om-1.8/Angular_momentum) for angular momentum and is linked to a URI for the concept `angular momentum`. A website may use the symbol [$H$](http://www.wurvoc.org/vocabularies/om-1.8/Angular_momentum) for angular momentum and link to the same concept `angular momentum` using the same URI. As both symbols are linked to the same concept, they are both disambiguated.

I've been working together with Hajo Rijgersberg ([see his PhD thesis](https://www.cs.vu.nl/en/Images/H%20Rijgersberg%2021mei2013_tcm75-342356.pdf)) on the [Ontology of Units of Measure](http://www.wurvoc.org/vocabularies/om-1.8/), which is an ontology with a large number of quantities and units.
**This ontology can be used as a list of quantities and their symbols.** But it is by no means complete.

One way we could use such an ontology is to insert the identifier (URI) into the text. At the [SWAIE workshop](http://swaie2014.wordpress.com), I outlined a method to do just that in LaTeX ([paper](http://ceur-ws.org/Vol-925/paper_5.pdf)). The physical symbols in the PDF output are then linked to the concept. Clicking on the symbol will cause a browser to open at the URL identifying the physical concept. At the moment I'm trying to implement this in MathJax, but I am finding some [technical difficulties](https://stackoverflow.com/questions/24514895/how-to-keep-rdfa-attributes-in-mathml-using-mathjax?noredirect=1#comment41599340_24514895).

> **Comments:**
> **username_0**: @Dieudonne.Thanks. It certainly would be useful sometimes to be able to link from a symbol to a concept URI.  It is surprising to me how many texts do not even include a list of symbols used.  

---

