<?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>S0035-001X2022000600007</article-id>
<article-id pub-id-type="doi">10.31349/revmexfis.68.060702</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Relativistic hyperbolic motion and its higher order kinematic quantities]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Pérez-Román]]></surname>
<given-names><![CDATA[I]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Rosu]]></surname>
<given-names><![CDATA[H. C.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Instituto Potosino de Investigación Científica y Tecnológica  ]]></institution>
<addr-line><![CDATA[San Luis Potosí S.L.P.]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2022</year>
</pub-date>
<volume>68</volume>
<numero>6</numero>
<fpage>0</fpage>
<lpage>0</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0035-001X2022000600007&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0035-001X2022000600007&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0035-001X2022000600007&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract We investigate the kinematics of the motion of an observer with constant proper acceleration (relativistic hyperbolic motion) in 1 + 1 and 1 + 3 dimensional Minkowski spacetimes. We provide explicit formulas for all the kinematic quantities up to the fourth proper time derivative (the Snap). In the 1 + 3 case, following a recent work of Pons and de Palol [Gen. Rel. Grav. 51 (2019) 80], a vectorial differential equation for the acceleration is obtained which by considering constant proper acceleration is turned into a nonlinear second order differential equation in terms of derivatives of the radius vector. If, furthermore, the velocity is parameterized in terms of hyperbolic functions, one obtains a differential equation to solve for the argument f(s) of the velocity. Differently from Pons and de Palol, who employed the particular solution, linear in the proper time s, we obtain the general solution and use it to work out more general expressions for the kinematical quantities. As a byproduct, we obtain a class of modified Rindler hyperbolic worldlines characterized by supplementary contributions to the components of the kinematical quantities.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Hyperbolic motion]]></kwd>
<kwd lng="en"><![CDATA[jerk]]></kwd>
<kwd lng="en"><![CDATA[snap]]></kwd>
<kwd lng="en"><![CDATA[Minkowski spacetime]]></kwd>
<kwd lng="en"><![CDATA[modified Rindler hyperbolas]]></kwd>
</kwd-group>
</article-meta>
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