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QuantityVariableDimensions[quantityvariable]

返回与指定 quantityvariable 相关联的基本量纲的列表.

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范例  
基本范例  
范围  
应用  
属性和关系  
可能存在的问题  
巧妙范例  
参见
相关指南
历史
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QuantityVariableDimensions

QuantityVariableDimensions[quantityvariable]

返回与指定 quantityvariable 相关联的基本量纲的列表.

更多信息

  • QuantityVariableDimensions 返回有序量纲对的列表，表明物理量纲中 quantityvariable 的幅度.
  • quantityvariable 可以是 QuantityVariable、QuantityVariable 对象的组合、或 QuantityVariable 的 Derivative. quantityvariable 也可包括 "PhysicalQuantity" 实体.
  • 物理量纲包括："AmountUnit"、"AngleUnit"、"ElectricCurrentUnit"、"InformationUnit"、"LengthUnit"、"LuminousIntensityUnit"、"MassUnit"、"MoneyUnit"、"SolidAngleUnit"、"TemperatureDifferenceUnit"、"TemperatureUnit" 和 "TimeUnit".
  • 电磁尺寸遵循SI惯例.

范例

打开所有单元 关闭所有单元

基本范例  (2)

求 QuantityVariable 的物理量纲：

Wolfram Language code: QuantityVariableDimensions[QuantityVariable["Φ", "RadiantFluxDensity"]]

使用 QuantityVariable 的单参数格式：

Wolfram Language code: QuantityVariableDimensions[QuantityVariable["RadiantFluxDensity"]]
Wolfram Language code: QuantityVariableDimensions[QuantityVariable["ElectricPotential"]]
Wolfram Language code: QuantityVariableDimensions[QuantityVariable["Temperature"]]

范围  (3)

求 QuantityVariable 对象组合的物理量纲：

Wolfram Language code: QuantityVariableDimensions[QuantityVariable["RadiantFluxDensity"] ^ 2]
Wolfram Language code: QuantityVariableDimensions[QuantityVariable["RadiantFluxDensity"] ^ 2 / QuantityVariable["Time"]]

判断 QuantityVariable 的 Derivative 的物理量纲：

Wolfram Language code: QuantityVariableDimensions[QuantityVariable["RadiantFluxDensity"]'[QuantityVariable["Time"]]]
Wolfram Language code: QuantityVariableDimensions[QuantityVariable["RadiantFluxDensity"]''[QuantityVariable["Time"]]]

探索 QuantityVariable 对象和它们的导数的任意组合的量纲：

Wolfram Language code: QuantityVariableDimensions[QuantityVariable["RadiantFluxDensity"]''[QuantityVariable["Time"]] / QuantityVariable["Speed"]]

应用  (2)

求电子物理量的采样的量纲系数：

Wolfram Language code: pqs = {#, QuantityVariableDimensions[QuantityVariable[#]]}& /@ {"ElectricCapacitance", "ElectricConductivity", "ElectricCurrent", "ElectricPotential", "ElectricResistance", "ElectricResistivity", "MagneticInductance", "MagneticInduction"}; Grid[Prepend[Flatten[{First[#], {Cases[Last[#], {"ElectricCurrentUnit", x_} :> x], Cases[Last[#], {"LengthUnit", x_} :> x], Cases[Last[#], {"MassUnit", x_} :> x], Cases[Last[#], {"TimeUnit", x_} :> x]} /. {} -> 0}]& /@ pqs, {"Physical Quantities", "Current", "Length", "Mass", "Time"}], Frame -> All]

检查量纲一致性的方程：

Wolfram Language code: FormulaData["NewtonsLawOfUniversalGravitation"]
Wolfram Language code: qv = {#, QuantityVariableDimensions[#]}& /@ FormulaData["NewtonsLawOfUniversalGravitation", "QuantityVariables"]

基于量纲以标准格式定义变量：

Wolfram Language code: mass = {{"LengthUnit", 0}, {"MassUnit", 1}, {"TimeUnit", 0}}; distance = {{"LengthUnit", 1}, {"MassUnit", 0}, {"TimeUnit", 0}}; force = {{"LengthUnit", 1}, {"MassUnit", 1}, {"TimeUnit", -2}};

检查公式在量纲上是否正确：

Wolfram Language code: force === UnitDimensions[Quantity[1, "GravitationalConstant"]] + 2 * mass - 2 * distance

属性和关系  (2)

也可以确定 "PhysicalQuantity" 实体的维度：

Wolfram Language code: QuantityVariableDimensions[Entity["PhysicalQuantity", "Length"]]

用 ResourceFunction "PhysicalQuantityLookup" 根据单位量纲求物理量：

Wolfram Language code: ResourceFunction["PhysicalQuantityLookup"][{{"LengthUnit", -1}, {"LuminousIntensityUnit", 1}}, "QuantityVariableName"]

可能存在的问题  (2)

一些物理量是没有量纲的：

Wolfram Language code: QuantityVariableDimensions[QuantityVariable["ϵ", "MultiplicativeConstants"]]

对于 QuantityVariable 的函数，只对头部返回量纲：

Wolfram Language code: QuantityVariableDimensions[x[t]]

求导数的量纲：

Wolfram Language code: QuantityVariableDimensions[QuantityVariable["E", "Energy"]'[QuantityVariable["t", "Time"]]]

巧妙范例  (2)

探索机械的共同物理量的空间：

Wolfram Language code: mechanicspqs = {#, QuantityVariableDimensions[QuantityVariable[#]]}& /@ {"AngularMomentum", "Energy", "Force", "Frequency", "GravitationalAcceleration", "Length", "Mass", "MassDensity", "MomentOfInertia", "Period", "Power", "Speed", "SpringConstant", "Stress", "Time", "Volume"}; mechanicsdimensions = ({#[[1]], {"LengthUnit", "MassUnit", "TimeUnit"} /. MapThread[Rule, Transpose[#[[2]]]]}& /@ mechanicspqs) /. {"LengthUnit" -> 0, "MassUnit" -> 0, "TimeUnit" -> 0}; Graphics3D[{PointSize[Medium], Blue, Tooltip[Point[#[[2]]], #[[1]]]& /@ mechanicsdimensions}, Axes -> True, Ticks -> Table[i, {3}, {i, -3, 3}], AxesLabel -> {"length", "mass", "time"}, BoxRatios -> 1]

只用这些物理量，基于量纲分析估计炸弹爆炸的能量：

Wolfram Language code: pqs = {QuantityVariable["Energy"], QuantityVariable["MassDensity"], QuantityVariable["Radius"], QuantityVariable["Time"]};

求这些物理量的量纲：

Wolfram Language code: pqdimensions = {#, QuantityVariableDimensions[#]}& /@ pqs;
Wolfram Language code: Grid[Prepend[Flatten[{First[#], {Cases[Last[#], {"LengthUnit", x_} :> x], Cases[Last[#], {"MassUnit", x_} :> x], Cases[Last[#], {"TimeUnit", x_} :> x]} /. {} -> 0}]& /@ pqdimensions, {"Physical Quantities", "LengthUnit", "MassUnit", "TimeUnit"}], Frame -> All]

编写涉及物理量的量纲方程：

Wolfram Language code: dimensionrules = (#1 -> Times @@((Power@@@#2)))& @@@ pqdimensions

将能量拟设为半径、质量、时间和质量密度的函数：

Wolfram Language code: energyansatz = QuantityVariable["Energy"] == constant QuantityVariable["MassDensity"] ^ β QuantityVariable["Radius"] ^ γ QuantityVariable["Time"] ^ δ

形成并且求解指数的线性方程：

Wolfram Language code: PowerExpand[Log /@ (energyansatz /. dimensionrules)]
Wolfram Language code: SolveAlways[%, {Log["LengthUnit"], Log["TimeUnit"], Log["MassUnit"]}]
Wolfram Language code: energyansatz /. First[%]

给出给定时间上的参数输入，估计爆炸的能量：

Wolfram Language code: constant = 1; massdensity = Quantity[1.2, "Kilograms" / "Meters" ^ 3]; radius = Quantity[80, "Meters"]; time = Quantity[0.006, "Seconds"];
Wolfram Language code: energy = (constant massdensity radius^5/time^2)
Wolfram Language code: UnitConvert[energy, "KilotonsOfTNT"]
Wolfram Research (2014)，QuantityVariableDimensions，Wolfram 语言函数，https://reference.wolfram.com/language/ref/QuantityVariableDimensions.html （更新于 2018 年）.

文本

Wolfram Research (2014)，QuantityVariableDimensions，Wolfram 语言函数，https://reference.wolfram.com/language/ref/QuantityVariableDimensions.html （更新于 2018 年）.

CMS

Wolfram 语言. 2014. "QuantityVariableDimensions." Wolfram 语言与系统参考资料中心. Wolfram Research. 最新版本 2018. https://reference.wolfram.com/language/ref/QuantityVariableDimensions.html.

APA

Wolfram 语言. (2014). QuantityVariableDimensions. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/QuantityVariableDimensions.html 年

BibTeX

@misc{reference.wolfram_2026_quantityvariabledimensions, author="Wolfram Research", title="{QuantityVariableDimensions}", year="2018", howpublished="\url{https://reference.wolfram.com/language/ref/QuantityVariableDimensions.html}", note=[Accessed: 03-July-2026]}

BibLaTeX

@online{reference.wolfram_2026_quantityvariabledimensions, organization={Wolfram Research}, title={QuantityVariableDimensions}, year={2018}, url={https://reference.wolfram.com/language/ref/QuantityVariableDimensions.html}, note=[Accessed: 03-July-2026]}