Difference between revisions of "Dictionary:State variable"

From SEG Wiki
Jump to: navigation, search
(Prepared the page for translation)
(Marked this version for translation)
 
Line 3: Line 3:
 
</translate>
 
</translate>
 
{{lowercase}}
 
{{lowercase}}
<translate>{{#category_index:S|state variable}}
+
<translate><!--T:1-->
 +
{{#category_index:S|state variable}}
 
One of the sets of variables which completely describe a system at any time. A state variable may represent a derivative of a quantity which is itself a state variable, allowing differential equations to be expressed as a set of linear simultaneous equations. For example, the voltage drop around an electrical circuit which includes capacitance, inductance, and resistance may be expressed by the differential equation:  
 
One of the sets of variables which completely describe a system at any time. A state variable may represent a derivative of a quantity which is itself a state variable, allowing differential equations to be expressed as a set of linear simultaneous equations. For example, the voltage drop around an electrical circuit which includes capacitance, inductance, and resistance may be expressed by the differential equation:  
  
 +
<!--T:2-->
 
<center><math> E(t)=RI + L\frac{dI}{dt} +C\int_t I dt</math>. </center>  
 
<center><math> E(t)=RI + L\frac{dI}{dt} +C\int_t I dt</math>. </center>  
  
 +
<!--T:3-->
 
Using state variables of <math display="inline">I </math>, <math display="inline">Q=\int I dt </math>, and <math display="inline">P=\frac{dI}{dt}</math> permits this to be written as a set of three simultaneous equations:  
 
Using state variables of <math display="inline">I </math>, <math display="inline">Q=\int I dt </math>, and <math display="inline">P=\frac{dI}{dt}</math> permits this to be written as a set of three simultaneous equations:  
  
  
 +
<!--T:4-->
 
<center><math>E(t)=RI+LP+CQ </math>,
 
<center><math>E(t)=RI+LP+CQ </math>,
  
  
 +
<!--T:5-->
 
<math>\frac{dQ}{dt}=I</math>, and  
 
<math>\frac{dQ}{dt}=I</math>, and  
  
  
 +
<!--T:6-->
 
<math>\frac{dI}{dt}=P </math>.</center>
 
<math>\frac{dI}{dt}=P </math>.</center>
  
  
 +
<!--T:7-->
 
See also [[Special:MyLanguage/Dictionary:parameter|''parameter'']].
 
See also [[Special:MyLanguage/Dictionary:parameter|''parameter'']].
 
</translate>
 
</translate>

Latest revision as of 03:00, 28 January 2018

Other languages:
English • ‎español


One of the sets of variables which completely describe a system at any time. A state variable may represent a derivative of a quantity which is itself a state variable, allowing differential equations to be expressed as a set of linear simultaneous equations. For example, the voltage drop around an electrical circuit which includes capacitance, inductance, and resistance may be expressed by the differential equation:

.

Using state variables of , , and permits this to be written as a set of three simultaneous equations:


,


, and


.


See also parameter.