OpenMath Content Dictionary: dimensions1

Canonical URL:

http://www.openmath.org/cd/dimensions1.ocd

CD Base:

http://www.openmath.org/cd

CD File:

dimensions1.ocd

CD as XML Encoded OpenMath:

dimensions1.omcd

Defines:

acceleration, area, charge, concentration, current, density, displacement, energy, force, length, mass, momentum, pressure, resistance, speed, temperature, time, velocity, voltage, volume

Date:

2004-03-30

Version:

4

Review Date:

2006-03-30

Status:

experimental

     This document is distributed in the hope that it will be useful, 
     but WITHOUT ANY WARRANTY; without even the implied warranty of 
     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

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     document freely as a verbatim copy. Furthermore, the copyright
     holder permits you to develop any derived work from this document
     provided that the following conditions are met.
       a) The derived work acknowledges the fact that it is derived from
          this document, and maintains a prominent reference in the 
          work to the original source.
       b) The fact that the derived work is not the original OpenMath 
          document is stated prominently in the derived work.  Moreover if
          both this document and the derived work are Content Dictionaries
          then the derived work must include a different CDName element,
          chosen so that it cannot be confused with any works adopted by
          the OpenMath Society.  In particular, if there is a Content 
          Dictionary Group whose name is, for example, `math' containing
          Content Dictionaries named `math1', `math2' etc., then you should 
          not name a derived Content Dictionary `mathN' where N is an integer.
          However you are free to name it `private_mathN' or some such.  This
          is because the names `mathN' may be used by the OpenMath Society
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       c) The derived work is distributed under terms that allow the
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     If you have questions about this license please contact the OpenMath
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This CD defines symbols which represent basic physical dimensions.

length

Role:

constant

Description:

This symbol represents the length physical dimension.

Signatures:

sts

area

Role:

constant

Description:

This symbol represents the area physical dimension.

Commented Mathematical property (CMP):

area = length*length

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="area"/>
    <OMA>
      <OMS cd="arith1" name="times"/>
      <OMS cd="dimensions1" name="length"/>
      <OMS cd="dimensions1" name="length"/>
    </OMA>
  </OMA>
</OMOBJ>

eq (area, times (length, length) )

$$\mathrm{area}=\mathrm{length}\times \mathrm{length}$$

Signatures:

sts

volume

Role:

constant

Description:

This symbol represents the volume physical dimension.

Commented Mathematical property (CMP):

volume = length*length*length

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="volume"/>
    <OMA>
      <OMS cd="arith1" name="times"/>
      <OMS cd="dimensions1" name="length"/>
      <OMS cd="dimensions1" name="length"/>
      <OMS cd="dimensions1" name="length"/>
    </OMA>
  </OMA>
</OMOBJ>

eq (volume, times (length, length, length) )

$$\mathrm{volume}=\mathrm{length}\times \mathrm{length}\times \mathrm{length}$$

Signatures:

sts

speed

Role:

constant

Description:

This symbol represents the speed physical dimension. It is the size of the derivative of distance with respect to time.

Commented Mathematical property (CMP):

speed = length/time

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="speed"/>
    <OMA>
      <OMS cd="arith1" name="divide"/>
      <OMS cd="dimensions1" name="length"/>
      <OMS cd="dimensions1" name="time"/>
    </OMA>
  </OMA>
</OMOBJ>

eq (speed, divide (length, time) )

$$\mathrm{speed}=\frac{\mathrm{length}}{\mathrm{time}}$$

Signatures:

sts

displacement

Role:

constant

Description:

This symbol represents the spatial difference between two points. The direction of the displacement is taken into account as well as the distance between the points.

Signatures:

sts

velocity

Role:

constant

Description:

This symbol represents the velocity physical dimension. It is the derivative of distance with respect to time.

Commented Mathematical property (CMP):

velocity = displacement/time

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
      <OMA>
        <OMS cd="relation1" name="eq"/>
        <OMS cd="dimensions1" name="velocity"/>
        <OMA>
          <OMS cd="arith1" name="divide"/>
          <OMS cd="dimensions1" name="displacement"/>
          <OMS cd="dimensions1" name="time"/>
        </OMA>
      </OMA>
    </OMOBJ>

eq (velocity, divide (displacement, time) )

$$\mathrm{velocity}=\frac{\mathrm{displacement}}{\mathrm{time}}$$

Signatures:

sts

acceleration

Role:

constant

Description:

This symbol represents the acceleration physical dimension. It is the second derivative of distance with respect to time.

Commented Mathematical property (CMP):

acceleration = displacement/(time^2)

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="acceleration"/>
    <OMA>
      <OMS cd="arith1" name="divide"/>
      <OMS cd="dimensions1" name="displacement"/>
      <OMA>
        <OMS cd="arith1" name="power"/>
        <OMS cd="dimensions1" name="time"/>
        <OMI> 2 </OMI>
      </OMA>
    </OMA>
  </OMA>
</OMOBJ>

eq (acceleration, divide (displacement, power (time, 2 ) ) )

$$\mathrm{acceleration}=\frac{\mathrm{displacement}}{{\mathrm{time}}^2}$$

Signatures:

sts

time

Role:

constant

Description:

This symbol represents the time physical dimension.

Signatures:

sts

mass

Role:

constant

Description:

This symbol represents the mass physical dimension.

Signatures:

sts

force

Role:

constant

Description:

This symbol represents the force physical dimension.

Commented Mathematical property (CMP):

force = mass*length/time^2

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="force"/>
    <OMA>
      <OMS cd="arith1" name="times"/>
      <OMS cd="dimensions1" name="mass"/>
      <OMA>
        <OMS cd="arith1" name="divide"/>
        <OMS cd="dimensions1" name="length"/>
        <OMA>
          <OMS cd="arith1" name="power"/>
          <OMS cd="dimensions1" name="time"/>
          <OMI> 2 </OMI>
        </OMA>
      </OMA>
    </OMA>
  </OMA>
</OMOBJ>

eq (force, times (mass, divide (length, power (time, 2 ) ) ) )

$$\mathrm{force}=\mathrm{mass}\frac{\mathrm{length}}{{\mathrm{time}}^2}$$

Signatures:

sts

temperature

Role:

constant

Description:

This symbol represents the temperature physical dimension.

Signatures:

sts

pressure

Role:

constant

Description:

This symbol represents the pressure physical dimension.

Commented Mathematical property (CMP):

pressure = force/area

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="pressure"/>
    <OMA>
      <OMS cd="arith1" name="divide"/>
      <OMS cd="dimensions1" name="force"/>
      <OMS cd="dimensions1" name="area"/>
    </OMA>
  </OMA>
</OMOBJ>

eq (pressure, divide (force, area) )

$$\mathrm{pressure}=\frac{\mathrm{force}}{\mathrm{area}}$$

Signatures:

sts

charge

Role:

constant

Description:

This symbol represents the charge physical dimension.

Commented Mathematical property (CMP):

charge = current/voltage

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="charge"/>
    <OMA>
      <OMS cd="arith1" name="divide"/>
      <OMS cd="dimensions1" name="current"/>
      <OMS cd="dimensions1" name="voltage"/>
    </OMA>
  </OMA>
</OMOBJ>

eq (charge, divide (current, voltage) )

$$\mathrm{charge}=\frac{\mathrm{current}}{\mathrm{voltage}}$$

Signatures:

sts

current

Role:

constant

Description:

This symbol represents the current physical dimension.

Commented Mathematical property (CMP):

current = voltage*charge

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="current"/>
    <OMA>
      <OMS cd="arith1" name="times"/>
      <OMS cd="dimensions1" name="voltage"/>
      <OMS cd="dimensions1" name="charge"/>
    </OMA>
  </OMA>
</OMOBJ>

eq (current, times (voltage, charge) )

$$\mathrm{current}=\mathrm{voltage}\times \mathrm{charge}$$

Signatures:

sts

voltage

Role:

constant

Description:

This symbol represents the voltage physical dimension.

Commented Mathematical property (CMP):

voltage = current/charge

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="voltage"/>
    <OMA>
      <OMS cd="arith1" name="divide"/>
      <OMS cd="dimensions1" name="current"/>
      <OMS cd="dimensions1" name="charge"/>
    </OMA>
  </OMA>
</OMOBJ>

eq (voltage, divide (current, charge) )

$$\mathrm{voltage}=\frac{\mathrm{current}}{\mathrm{charge}}$$

Signatures:

sts

resistance

Role:

constant

Description:

This symbol represents the resistance physical dimension, it is the resistance that an electrical circuit has to flow of charge.

Commented Mathematical property (CMP):

resistance = voltage/current

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="resistance"/>
    <OMA>
      <OMS cd="arith1" name="divide"/>
      <OMS cd="dimensions1" name="voltage"/>
      <OMS cd="dimensions1" name="current"/>
    </OMA>
  </OMA>
</OMOBJ>

eq (resistance, divide (voltage, current) )

$$\mathrm{resistance}=\frac{\mathrm{voltage}}{\mathrm{current}}$$

Signatures:

sts

density

Role:

constant

Description:

This symbol represents the density physical dimension, it is the mass per unit volume.

Commented Mathematical property (CMP):

density = mass/volume

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="density"/>
    <OMA>
      <OMS cd="arith1" name="divide"/>
      <OMS cd="dimensions1" name="mass"/>
      <OMS cd="dimensions1" name="volume"/>
    </OMA>
  </OMA>
</OMOBJ>

eq (density, divide (mass, volume) )

$$\mathrm{density}=\frac{\mathrm{mass}}{\mathrm{volume}}$$

Signatures:

sts

energy

Role:

constant

Description:

This symbol represents the energy physical dimension.

Commented Mathematical property (CMP):

energy = mass*length^2/time^2

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="energy"/>
    <OMA>
      <OMS cd="arith1" name="divide"/>
      <OMA>
        <OMS cd="arith1" name="times"/>
        <OMS cd="dimensions1" name="mass"/>
        <OMA>
          <OMS cd="arith1" name="power"/>
          <OMS cd="dimensions1" name="length"/>
          <OMI> 2 </OMI>
        </OMA>
      </OMA>
      <OMA>
        <OMS cd="arith1" name="power"/>
        <OMS cd="dimensions1" name="time"/>
        <OMI> 2 </OMI>
      </OMA>
    </OMA>
  </OMA>
</OMOBJ>

eq (energy, divide (times (mass, power (length, 2 ) ) , power (time, 2 ) ) )

$$\mathrm{energy}=\frac{\mathrm{mass}{\mathrm{length}}^2}{{\mathrm{time}}^2}$$

Signatures:

sts

concentration

Role:

constant

Description:

This symbol represents the concentration physical dimension, it is the amount of a substance in a volume.

Commented Mathematical property (CMP):

concentration = mass/length^3

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="concentration"/>
    <OMA>
      <OMS cd="arith1" name="divide"/>
      <OMS cd="dimensions1" name="mass"/>
      <OMA>
        <OMS cd="arith1" name="power"/>
        <OMS cd="dimensions1" name="length"/>
        <OMI> 3 </OMI>
      </OMA>
    </OMA>
  </OMA>
</OMOBJ>

eq (concentration, divide (mass, power (length, 3 ) ) )

$$\mathrm{concentration}=\frac{\mathrm{mass}}{{\mathrm{length}}^3}$$

Signatures:

sts

momentum

Role:

constant

Description:

This symbol represents the momentum physical dimension, it is mass times velocity.

Commented Mathematical property (CMP):

momentum = mass*velocity

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="momentum"/>
    <OMA>
      <OMS cd="arith1" name="times"/>
      <OMS cd="dimensions1" name="mass"/>
      <OMS cd="dimensions1" name="velocity"/>
    </OMA>
  </OMA>
</OMOBJ>

eq (momentum, times (mass, velocity) )

$$\mathrm{momentum}=\mathrm{mass}\times \mathrm{velocity}$$

Signatures:

sts