lua-physical

Author: Thomas Jenni

Version: 1.0.5

Date: 2021-05-08

License: MIT

This is a pure Lua library which provides functions and object for doing computation with physical quantities.

In general, a physical quantity consists of a numerical value called magnitude and a unit. There are restrictions to the allowed mathematical operations with physical quantities. For example the quantity time cannot be added to the quantity mass. Furthermore, new quantities can be obtained by multiplication or division from other base quantities. The density is such an example. It can be calculated by dividing the mass of a body by its volume.

Usage

The library can be loaded with the command require("physical"). Like probably no other Lua library, lua-physical pollutes the global namespace with objects that represent physical units. This is in order to simplify the entry of physical quantities. By convention, each unit starts with an underscore in order to distinguish them from other variables. A basic example is the following:

> require("physical")
> a = 1.4 * _m
> b = 2 * _m
> A = (a*b):to(_m^2)
> print(A)
2.8 * _m^2

In the above example, two length a and b are defined and then multiplied. The result is an area. The unit of this area is _m*_m and has to be explicitly converted to _m^2 be the :to() command. The next example is slightly more complicated.

> require("physical")
> m1 = 22 * _kg
> m2 = 5.972e24 * _kg
> r = 6371 * _km
> F_G = (_Gc * m1 * m2 / r^2):to(_N)
> print(F_G)
2.16032(10)e2 * _N

The goal of the above example is to calculate the gravitational force on a body with mass 22 kg sitting on the surface of the earth. As one can see, the result is given with an uncertainty in parentheses. This is because the gravitational constant is not exactly known. Lua-physical can deal with uncertainties. One can give an uncertainty explicitly by instantiating physical.Number().

Temperature units

Temperatur units as _degC or _degF are treated as temperature differences. An absolute conversion can be done and has to be called explicitly. The :to()-function has therefore a second argument, which is by default false. That means temperatures are by default treated as temperature differences. If it is true, absolute conversion is used.

> physical = require("physical")
> T_1 = 15 * _degC
> print(T_1)
15 * _degC
> print(T_1:to(_K))
15.0 * _K
> print(T_1:to(_K,true))
288.15 * _K

Uncertainty

> physical = require("physical")
> a = physical.Number(2,0.1) * _m
> A = (a^2):to(_m^2)
> V = (a^3):to(_m^3)
> print(a)
2.00(10) * _m
> print(A)
4.0(4) * _m^2
> print(V)
8.0(12) * _m^3

The uncertainty gets propagated by the Gaussian rule for completely uncorrelated uncertainties, i.e. they are added in quadrature. In the above example it is assumed, that the three sides of the cube were measured independently from each other and that the uncertainties of these measurements are not correlated. If one prefers another way of printing uncertainties, there are a few formatting options.

> physical = require("physical")
> local l = physical.Number(20.453,0.002) * _m

> physical.Number.format = physical.Number.SCIENTIFIC

> physical.Number.seperateUncertainty = true
> print(l)
(2.0453 +/- 0.0002)e1 * _m

> physical.Number.seperateUncertainty = false
> print(l)
2.0453(2)e1 * _m

> physical.Number.format = physical.Number.DECIMAL

> physical.Number.seperateUncertainty = true
> print(l)
(20.453 +/- 0.002) * _m

> physical.Number.seperateUncertainty = false
20.453(2) * _m

One can define, whether the uncertainty should be printed in the plus-minus notation or in the parentheses notation.

Latex

Since Latex now supports lua, this library is able to generate latex output. It uses the siunitx package notation, see ctan.org.

> physical = require("physical")
> E = 210 * _MeV
> print(E:tosiunitx())
\SI{210}{\mega\electronvolt}

Physical Data

Besides some physical constans, lua-physical has an isotope database. The data was taken from the Atomic Mass Evaluation - AME2016 by the Chinese Atomic Mass Data Center. The data was parsed and converted into a Lua table. One can access the data via the command physical.Data.Isotope(name,key).

> physical = require("physical")

> E_b = physical.Data.Isotope("235U","BindingEnergyPerNucleon")
> print(E_b)
7.590914(5)e3 * _keV

>  T_12 = physical.Data.Isotope("210Po","HalfLife")
>  print(T_12:to(_d))
1.38376(2)e2 * _d

List of Units and Prefixes

Base Units

The SI defines seven base units. For dimensionless quantities the unit _1 can be used.

Source: (NIST)http://physics.nist.gov/cuu/Units/units.html

SI-Prefixes

Most of the SI Units can have prefixes, i.e. _km, _hL, _ms, _uJ.

Source: (NIST)http://physics.nist.gov/cuu/Units/prefixes.html

Derived SI Units

Source: (NIST)http://physics.nist.gov/cuu/Units/units.html

Mathematical Constants

Physical Constants

Source: (NIST)http://physics.nist.gov/cuu/Constants/

Nominal Astronomical Units

Source: (IAU 2015 Resolution B3)https://www.iau.org/static/resolutions/IAU2015English.pdf

Non-SI Units accepted for use with the SI

Source: (NIST)http://physics.nist.gov/cuu/Units/outside.html

Other Metric Units

Source: (NIST)http://physics.nist.gov/cuu/Units/outside.html

Imperial Units

Source: (Wikipedia)https://en.wikipedia.org/wiki/Imperialunits

US Customary and Survey Units

Source: (Wikipedia)https://en.wikipedia.org/wiki/UnitedStatescustomaryunits