NondimensionalizationTransform

NondimensionalizationTransform[eq,ovars,fvars]

nondimensionalizes eq, replacing original variables ovars with the variables fvars.

NondimensionalizationTransform[eq,ovars,fvars,prop]

returns a property associated with the nondimensionalization of eq.

Details and Options

  • eq is an equation or differential equation constructed of Quantity and QuantityVariable objects or a list of such expressions.
  • ovars is a list of QuantityVariable objects present in eq.
  • fvars is a list of replacement variables for ovar.
  • In addition to the nondimensionalized equation, NondimensionalizationTransform can supply the rules for the "forward" transformation from the dimensional form to the nondimensional form and the "reverse" transformation from the new nondimensional form back to the original equation.
  • NondimensionalizationTransform supports the following properties:
  • "DimensionalizationMultipliers"Association of multipliers for the reverse transformation
    "DimensionalizationRules"list of rules for reversing the transformation
    "NondimensionalizationMultipliers"Association of multipliers for the transformed variables
    "NondimensionalizationRules"list of rules for nondimensionalizing the equation
    "ReducedForm"the nondimensionalized equation
  • Alternatively "PropertyAssociation" can be used to return an Association of the properties.
  • NondimensionalizationTransform returns "ReducedForm" by default.
  • The following options can be given:
  • GeneratedParametersChow to name generated replacement variables
    GeneratedQuantityMagnitudesKhow to name generated quantity factors
    IncludeQuantities{}additional quantities to include
    UnitSystemAutomaticunit system used to generate factors
  • The GeneratedQuantityMagnitudes setting is used in cases where it is not possible to remove all dimensions from a variable using the QuantityVariable and Quantity objects within the equation. In those cases, new quantities are added to the solution with the symbol provided by the GeneratedQuantityMagnitudes option.
  • The GeneratedParameters setting is used when there are additional QuantityVariable objects within the equation not included in ovar. NondimensionalizationTransform removes all QuantityVariable objects from an equation. Additional QuantityVariable objects are replaced by variables as specified by the GeneratedParameters option.
  • IncludeQuantities adds additional Quantity objects to use in generating dimensionless solutions.
  • UnitSystem controls the unit system to use for generating multiplicative factors when removing dimensions from the equation. With Automatic, NondimensionalizationTransform creates the factors from the units and physical quantities present in the equation or specified by IncludeQuantities.
  • UnitSystem can also be set to use a natural units system. These options include "DeSitterUnits", "GaussianNaturalUnits", "GaussianQuantumChromodynamicsUnits", "HartreeAtomicUnits", "LorentzHeavisideNaturalUnits", "LorentzHeavisideQuantumChromodynamicsUnits", "PlanckUnits", "RydbergAtomicUnits" and "StonyUnits".
  • The units and values for "DeSitterUnits" are:
  • "LengthUnit"
    "MassUnit"
    "TimeUnit"
    "TemperatureUnit"
    "ElectricCurrentUnit"
  • The units and values for "GaussianNaturalUnits" are:
  • "LengthUnit"
    "MassUnit"
    "TimeUnit"
    "TemperatureUnit"
    "ElectricCurrentUnit"
  • The units and values for "GaussianQuantumChromodynamicsUnits" are:
  • "LengthUnit"
    "MassUnit"
    "TimeUnit"
    "TemperatureUnit"
    "ElectricCurrentUnit"
  • The units and values for "HartreeAtomicUnits" are:
  • "LengthUnit"
    "MassUnit"
    "TimeUnit"
    "TemperatureUnit"
    "ElectricCurrentUnit"
  • The units and values for "LorentzHeavisideNaturalUnits" are:
  • "LengthUnit"
    "MassUnit"
    "TimeUnit"
    "TemperatureUnit"
    "ElectricCurrentUnit"
  • The units and values for "LorentzHeavisideQuantumChromodynamicsUnits" are:
  • "LengthUnit"
    "MassUnit"
    "TimeUnit"
    "TemperatureUnit"
    "ElectricCurrentUnit"
  • The units and values for "PlanckUnits" are:
  • "LengthUnit"
    "MassUnit"
    "TimeUnit"
    "TemperatureUnit"
    "ElectricCurrentUnit"
  • The units and values for "RydbergAtomicUnits" are:
  • "LengthUnit"
    "MassUnit"
    "TimeUnit"
    "TemperatureUnit"
    "ElectricCurrentUnit"
  • The units and values for "StonyUnits" are:
  • "LengthUnit"
    "MassUnit"
    "TimeUnit"
    "TemperatureUnit"
    "ElectricCurrentUnit"

Examples

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Basic Examples  (2)

Remove dimensions from the driven oscillator equation:

In[1]:=
Click for copyable input
Out[1]=

Compute the replacement rules for the wave equation that yields a dimensionless form:

In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
Out[2]=

Scope  (4)

Options  (4)

Applications  (4)

Properties & Relations  (1)

Possible Issues  (3)

Neat Examples  (1)

See Also

QuantityVariable  QuantityVariableDimensions  DimensionalCombinations

Introduced in 2018
(11.3)