Converting Longitude and Latitude into Meters

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Solistics
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Hi, I'm trying to convert latitude and longitude into meters (x,y). I was thinking of UTM however I don't understand the equations as the ones I've seen just go on forever. Could someone help me understand how to use these equations?

heres the website that I've been trying to understand: http://www.uwgb.edu/dutchs/UsefulData/UTMFormulas.HTM

Thanks
 
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How accurately do you need to do it and over what area?
It may be enough to just use the X,Y position (in your chosen coord system) of a nearby lat/long point and just do differences from there assuming the Earth is flat
 
The area is fairly small as I'm using this for an autonomous robot application so the accuracy I'm trying to reach is as presice as I can (a few meters). I'm giving it points that it has to go to and it has a GPS to give it longitude and Latitude. By converting longitude and latitude to meters would make my life a lot easier to work.
 
Choose a latitude [tex]\phi_0[/tex] and longitude [tex]\theta_0[/tex] as the origin of your local coordinate system, then

[tex]y = R \; \Delta \phi[/tex]
and
[tex]x = R \; \Delta \theta \; \cos(\phi_0)[/tex]

where R = the radius of the Earth in your chosen units, with latitude and longitude in radians.