Systems of Units - Maple Help

Systems of Units

 This document describes the systems of units used for unit conversions and in the Units environments (default, Natural, Simple, and Standard).
 •
 •
 •
 •

Definition

 A system of units is a set of related units that are used for calculations. The system includes base units, which represent base dimensions, and derived units, which represent products of powers of base dimensions. Some units exist in more than one system of units. For example, there is a unit of mass named the ounce in the avoirdupois and troy systems of units. To distinguish between these units in Maple, each unit has a context. For example, the ounce[avoirdupois] and ounce[troy] are units of mass. For additional information about dimensions, units, and contexts, see Details.
 For example, in the MKS system, the base units are the meter, kilogram, and second, which represent the base dimensions of length, mass, and time, respectively.  In this system, the unit of speed is the meter per second. However, the unit of force, the kilogram meter per square second, is named the newton.
 In the FPS system, the base units are the foot, pound, and second, which represent the base dimensions of length, mass, and time, respectively. The complex unit of speed and derived unit of force are the foot per second and poundal, respectively, where 1 poundal equals 1 foot pound per second squared.

Systems of Units

 The set of systems of units in Maple is:

SI (International System of Units) (meter-kilogram-second-ampere-kelvin-mole-candela)

FPS (foot-pound-second)

MKS (meter-kilogram-second)

CGS (centimeter-gram-second)

EMU (Electromagnetic) (centimeter-gram-second-abampere)

ESU (Electrostatic) (centimeter-gram-second-abcoulomb)

Atomic (bohr-electron mass-atomic second-electron)

MTS (meter-tonne-second)

Converting to a System

 The convert/system command converts a unit to the default unit with the same dimension in the specified system of units.

Working with Systems of Units

 The following Units package functions manage the systems of units.

Examples

 > $\mathrm{with}\left(\mathrm{Units}\right):$
 The default system of units in Maple is SI.
 > $\mathrm{GetSystems}\left(\right)$
 ${\mathrm{Atomic}}{,}{\mathrm{CGS}}{,}{\mathrm{EMU}}{,}{\mathrm{ESU}}{,}{\mathrm{FPS}}{,}{\mathrm{MKS}}{,}{\mathrm{MTS}}{,}{\mathrm{SI}}$ (1)
 > $\mathrm{UsingSystem}\left(\right)$
 ${\mathrm{SI}}$ (2)
 To develop a system of units based on the furlong, long hundredweight, and the fortnight, define a new (fictional) unit of force named the fortis, the derived unit of force equal to a furlong long hundredweight per fortnight squared.
 > $\mathrm{AddUnit}\left('\mathrm{fortis}','\mathrm{context}'='\mathrm{standard}','\mathrm{conversion}'=\frac{'\mathrm{furlong}''\mathrm{hundredweight}\left[\mathrm{long}\right]'}{{'\mathrm{fortnight}'}^{2}}\right)$
 > $\mathrm{AddSystem}\left('\mathrm{OldEnglish}','\mathrm{furlong}','\mathrm{hundredweight}\left[\mathrm{long}\right]','\mathrm{fortnight}','\mathrm{fortis}','\mathrm{fortis}''\mathrm{furlong}'\right)$
 > $\mathrm{GetSystems}\left(\right)$
 ${\mathrm{Atomic}}{,}{\mathrm{CGS}}{,}{\mathrm{EMU}}{,}{\mathrm{ESU}}{,}{\mathrm{FPS}}{,}{\mathrm{MKS}}{,}{\mathrm{MTS}}{,}{\mathrm{OldEnglish}}{,}{\mathrm{SI}}$ (3)
 In these examples, 32 newtons and 693 meters per day are converted to the appropriate units in the Old English system.
 If infolevel is set to a greater integer (possible settings are 1 through 5), more detailed information about the computation method is displayed.
 > $\mathrm{infolevel}\left[\mathrm{Units}\right]≔1:$
 > $\mathrm{convert}\left(32,'\mathrm{system}','N','\mathrm{OldEnglish}'\right)$
 convert/system:   "converting to the units fortis"
 $\frac{{41472000000000000000}}{{9052407727}}$ (4)
 > $\mathrm{convert}\left(693,'\mathrm{system}',\frac{'m'}{'\mathrm{day}'},'\mathrm{OldEnglish}'\right)$
 convert/system:   "converting to the units furlong/fortnight"
 $\frac{{6125}}{{127}}$ (5)
 > $\mathrm{unassign}\left('\mathrm{infolevel}\left[\mathrm{Units}\right]'\right):$
 Set the system OldEnglish as the default and perform the computations in the Units[Standard] environment.
 Notes:
 – To enter a unit in 2-D Math input, select the unit from the appropriate Units palette. If the unit you want is not there, select $\mathrm{unit}$ and then enter the unit.
 – When you edit a unit, double brackets appear around it.
 > $\mathrm{UseSystem}\left('\mathrm{OldEnglish}'\right)$
 > $\mathrm{with}\left(\mathrm{Units}\left[\mathrm{Standard}\right]\right):$
 > $23235\mathrm{Unit}\left(\frac{'m'}{'s'}\right)$
 ${23235}{}⟦\frac{{m}}{{s}}⟧$ (6)
 > $\mathrm{combine}\left(23235\mathrm{Unit}\left(\frac{'m'}{'s'}\right),'\mathrm{units}'\right)$
 $\frac{{195174000000}}{{1397}}{}⟦\frac{{\mathrm{furlong}}}{{\mathrm{fortnight}}}⟧$ (7)
 > $\mathrm{convert}\left(1.0\mathrm{Unit}\left(\frac{'\mathrm{cm}'}{'\mathrm{min}'}\right),'\mathrm{system}'\right)$
 ${1.002147459}{}⟦\frac{{\mathrm{furlong}}}{{\mathrm{fortnight}}}⟧$ (8)
 > $32.0\mathrm{Unit}\left('N'\right)$
 ${32.0}{}⟦{N}⟧$ (9)
 > $\mathrm{convert}\left(,'\mathrm{system}','\mathrm{OldEnglish}'\right)$
 ${4.581322588}{×}{{10}}^{{9}}{}⟦{\mathrm{fortis}}⟧$ (10)
 > $\mathrm{Unit}\left('\mathrm{ft}'\right)$
 ${6.941397861}{×}{{10}}^{{6}}{}⟦{\mathrm{fortis}}{}{\mathrm{furlong}}⟧$ (11)
 > $\frac{\mathrm{Unit}\left('\mathrm{day}'\right)}{}$
 ${9.717957005}{×}{{10}}^{{7}}{}⟦\frac{{{\mathrm{furlong}}}^{{2}}{}{{\mathrm{hundredweight}}}_{{\mathrm{long}}}}{{{\mathrm{fortnight}}}^{{3}}}⟧$ (12)
 > $\mathrm{convert}\left(,'\mathrm{units}','W'\right)$
 ${0.0001128888889}{}⟦{W}⟧$ (13)
 The system can also be removed from Maple, but first another system must be set as the default system.
 > $\mathrm{RemoveSystem}\left('\mathrm{OldEnglish}'\right):$
 > $\mathrm{UseSystem}\left('\mathrm{FPS}'\right):$
 > $\mathrm{RemoveSystem}\left('\mathrm{OldEnglish}'\right):$
 > $\mathrm{GetSystems}\left(\right)$
 ${\mathrm{Atomic}}{,}{\mathrm{CGS}}{,}{\mathrm{EMU}}{,}{\mathrm{ESU}}{,}{\mathrm{FPS}}{,}{\mathrm{MKS}}{,}{\mathrm{MTS}}{,}{\mathrm{SI}}$ (14)