quantitykind:HamiltonFunction

URI: http://qudt.org/vocab/quantitykind/HamiltonFunction

Type
Description

The Hamilton–Jacobi equation (HJE) is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations.

Properties
qudt:plainTextDescription
The Hamilton–Jacobi equation (HJE) is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations.
qudt:latexDefinition
$H = \sum p_i\dot{q_i} - L$, where $p_i$ is a generalized momentum, $\dot{q_i}$ is a generalized velocity, and $L$ is the Lagrange function.
Annotations
rdfs:comment
Applicable units are those of quantitykind:HamiltonFunction
dcterms:description
The Hamilton–Jacobi equation (HJE) is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations.
rdfs:label
Hamilton Function(en)
View as:  CSV

Work in progress

RDF/XML
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    xmlns:j.0="http://qudt.org/schema/qudt/"
    xmlns:j.1="http://purl.org/dc/terms/"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
  <rdf:Description rdf:about="http://qudt.org/vocab/quantitykind/HamiltonFunction">
    <j.0:latexDefinition rdf:datatype="http://qudt.org/schema/qudt/LatexString">$H = \sum p_i\dot{q_i} - L$, where $p_i$ is a generalized momentum, $\dot{q_i}$ is a generalized velocity, and $L$ is the Lagrange function.</j.0:latexDefinition>
    <rdfs:label xml:lang="en">Hamilton Function</rdfs:label>
    <j.0:hasDimensionVector rdf:resource="http://qudt.org/vocab/dimensionvector/A0E0L2I0M1H0T-2D0"/>
    <rdf:type rdf:resource="http://qudt.org/schema/qudt/QuantityKind"/>
    <rdfs:comment>Applicable units are those of quantitykind:HamiltonFunction</rdfs:comment>
    <j.0:symbol>H</j.0:symbol>
    <rdfs:isDefinedBy rdf:resource="http://qudt.org/2.1/vocab/quantitykind"/>
    <j.1:description rdf:datatype="http://qudt.org/schema/qudt/LatexString">The Hamilton–Jacobi equation (HJE) is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations.</j.1:description>
    <j.0:applicableUnit rdf:resource="http://qudt.org/vocab/unit/J"/>
    <j.0:applicableUnit rdf:resource="http://qudt.org/vocab/unit/PicoJ"/>
    <j.0:plainTextDescription>The Hamilton–Jacobi equation (HJE) is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations.</j.0:plainTextDescription>
    <j.0:informativeReference rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://en.wikipedia.org/wiki/Hamilton–Jacobi_equation</j.0:informativeReference>
    <j.0:isoNormativeReference rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://www.iso.org/iso/catalogue_detail?csnumber=31889</j.0:isoNormativeReference>
    <j.0:applicableUnit rdf:resource="http://qudt.org/vocab/unit/NanoJ"/>
  </rdf:Description>
</rdf:RDF>
TURTLE
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@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

<http://qudt.org/vocab/quantitykind/HamiltonFunction>
  rdf:type <http://qudt.org/schema/qudt/QuantityKind> ;
  <http://purl.org/dc/terms/description> "The Hamilton–Jacobi equation (HJE) is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations."^^<http://qudt.org/schema/qudt/LatexString> ;
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  <http://qudt.org/schema/qudt/applicableUnit> <http://qudt.org/vocab/unit/NanoJ> ;
  <http://qudt.org/schema/qudt/applicableUnit> <http://qudt.org/vocab/unit/PicoJ> ;
  <http://qudt.org/schema/qudt/hasDimensionVector> <http://qudt.org/vocab/dimensionvector/A0E0L2I0M1H0T-2D0> ;
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  <http://qudt.org/schema/qudt/isoNormativeReference> "http://www.iso.org/iso/catalogue_detail?csnumber=31889"^^xsd:anyURI ;
  <http://qudt.org/schema/qudt/latexDefinition> "$H = \\sum p_i\\dot{q_i} - L$, where $p_i$ is a generalized momentum, $\\dot{q_i}$ is a generalized velocity, and $L$ is the Lagrange function."^^<http://qudt.org/schema/qudt/LatexString> ;
  <http://qudt.org/schema/qudt/plainTextDescription> "The Hamilton–Jacobi equation (HJE) is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations." ;
  <http://qudt.org/schema/qudt/symbol> "H" ;
  rdfs:comment "Applicable units are those of quantitykind:HamiltonFunction" ;
  rdfs:isDefinedBy <http://qudt.org/2.1/vocab/quantitykind> ;
  rdfs:label "Hamilton Function"@en ;
.
JSON
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 ,"qname":"quantitykind:HamiltonFunction" 
 ,"uri":"http:\/\/qudt.org\/vocab\/quantitykind\/HamiltonFunction" 
 ,"properties":["applicable unit":"unit:J" 
    ,"applicable unit":"unit:NanoJ" 
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    ,"comment":"Applicable units are those of quantitykind:HamiltonFunction" 
    ,"description":"The Hamilton\u2013Jacobi equation (HJE) is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations." 
    ,"description (plain text)":"The Hamilton\u2013Jacobi equation (HJE) is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations." 
    ,"has dimension vector":"dimension:A0E0L2I0M1H0T-2D0" 
    ,"informative reference":"http:\/\/en.wikipedia.org\/wiki\/Hamilton\u2013Jacobi_equation" 
    ,"isDefinedBy":"&lt;http:\/\/qudt.org\/2.1\/vocab\/quantitykind&gt;" 
    ,"label":"Hamilton Function" 
    ,"latex definition":"$H = \\sum p_i\\dot{q_i} - L$, where $p_i$ is a generalized momentum, $\\dot{q_i}$ is a generalized velocity, and $L$ is the Lagrange function." 
    ,"normative reference (ISO)":"http:\/\/www.iso.org\/iso\/catalogue_detail?csnumber=31889" 
    ,"symbol":"H" 
    ,"type":"qudt:QuantityKind" 
    ]}
JSON-LD
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