<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0035-001X</journal-id>
<journal-title><![CDATA[Revista mexicana de física]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. fis.]]></abbrev-journal-title>
<issn>0035-001X</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Física]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0035-001X2017000100026</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Geometry of classical particles on curved surfaces]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Santiago]]></surname>
<given-names><![CDATA[J.A.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Chacón-Acosta]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[González-Gaxiola]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Torres-Vargas]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Autónoma Metropolitana  ]]></institution>
<addr-line><![CDATA[Cd. de México ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Autónoma Metropolitana  ]]></institution>
<addr-line><![CDATA[Cd. de México ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>02</month>
<year>2017</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>02</month>
<year>2017</year>
</pub-date>
<volume>63</volume>
<numero>1</numero>
<fpage>26</fpage>
<lpage>31</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0035-001X2017000100026&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0035-001X2017000100026&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0035-001X2017000100026&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract In this paper we consider a particle moving on a curved surface. From a variational principle, we write the equation of motion and the constraining force, both in terms of the Darboux frame adapted to the trajectory, that involves geometric information of the surface. By deformation of the trajectory on the surface, the constraining force and equation of motion of the perturbation are obtained. We show that the transversal deformation follows a generalized Raychaudhuri equation that contains extrinsic information besides the geodesic curvature. Results in the case of surface with axial symmetry can be parametrized in terms of the angular momenta.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen En este artículo consideramos el movimiento de una partícula sobre una superficie curvada. De un principio variacional, encontramos las ecuaciones de movimiento y la fuerza de constricción, en el marco de Darboux adaptado a la trayectoria. Deformando estas ecuaciones, encontramos que la perturbación transversal satisface una ecuación de Raychaudhuri generalizada que contiene información extrínseca además de la curvatura geodésica. En el caso de superficies con simetría axial, los resultados se pueden parametrizar en términos del momento angular.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Curves]]></kwd>
<kwd lng="en"><![CDATA[curved surfaces]]></kwd>
<kwd lng="en"><![CDATA[particle on surfaces]]></kwd>
<kwd lng="es"><![CDATA[Curvas]]></kwd>
<kwd lng="es"><![CDATA[superficies curvas]]></kwd>
<kwd lng="es"><![CDATA[partículas en superficies]]></kwd>
</kwd-group>
</article-meta>
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