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<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><i><span style="font-family:"Times New Roman","serif"">Sayın liste üyeleri,</span></i><span style="font-family:"Times New Roman","serif""><span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-family:"Times New Roman","serif""><span> </span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><i><span style="font-family:"Times New Roman","serif"">MSGSÜ Matematik Bölümü Genel
Seminerinde bu haftaki konuşmacımız Oğul Esen. Seminer ile ilgili tüm detaylar
aşağıda yer almaktadır. </span></i><span style="font-family:"Times New Roman","serif""><span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-family:"Times New Roman","serif""><span> </span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-family:"Times New Roman","serif""><span> </span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-family:"Times New Roman","serif"">Oğul Esen (Gebze Teknik
Üniversitesi)<span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-family:"Times New Roman","serif""><span> </span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-family:"Times New Roman","serif"">Başlık: " Matching of
(higher-order) Lagrangian dynamics"<span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-family:"Times New Roman","serif""><span> </span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-family:"Times New Roman","serif"">Özet: <span></span></span></p>
<p class="MsoNormal" style="margin:3pt 0cm;text-align:justify;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-family:"Times New Roman","serif";color:black">The talk will be consisting of two main parts. In the
first one, a gentle introduction to Geometric Mechanics will be presented.
Accordingly, some basic notions of the theory namely, Lie groups, Lie algebras,
Euler-Poincaré equations, will be exhibited. <br></span></p><p class="MsoNormal" style="margin:3pt 0cm;text-align:justify;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><br><span style="font-family:"Times New Roman","serif";color:black"><span></span></span></p>
<p class="MsoNormal" style="margin:3pt 0cm;text-align:justify;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-family:"Times New Roman","serif";color:black">In the second part, we shall address the problem of
determining the matched equations of motion of two interacting systems (whose
configuration spaces are Lie groups) governing the coupled system starting with
the individual equations of motions in (higher-order) Lagrangian form. The
configuration spaces of the systems being Lie groups is imperative here in
order to define the mutual actions. We shall present the theory of matched
dynamics and particularly write, what I call, (higher-order) matched
Euler-Poincaré equations. It will be shown that the theory of matched dynamics
is a generalization of the well-developed semi-direct product theory. <br></span></p><p class="MsoNormal" style="margin:3pt 0cm;text-align:justify;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><br><span style="font-family:"Times New Roman","serif";color:black"> <span></span></span></p>
<p class="MsoNormal" style="margin:3pt 0cm;text-align:justify;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-family:"Times New Roman","serif";color:black">This talk is part of a project pursued jointly Serkan
Sütlü.</span></p><p class="MsoNormal" style="margin:3pt 0cm;text-align:justify;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><br><span style="font-family:"Times New Roman","serif";color:black"> <span></span></span></p>
<p class="MsoNormal" style="margin:3pt 0cm;text-align:justify;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-family:"Times New Roman","serif";color:black">References<span></span></span></p>
<ul style="margin-bottom:0cm" type="disc"><li class="MsoNormal" style="color:black;line-height:normal;margin:0cm 0cm 10pt;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-family:"Times New Roman","serif";background:white none repeat scroll 0% 0%">O. Esen, Kudeyt, M., Sütlü, S. (2019).
Matched Higher Order Lagrangian Dynamics. arXiv preprint arXiv:1909.10375.</span><span style="font-family:"Times New Roman","serif""><span></span></span></li></ul>
<ul style="margin-bottom:0cm" type="disc"><li class="MsoNormal" style="color:black;line-height:normal;margin:0cm 0cm 10pt;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-family:"Times New Roman","serif";background:white none repeat scroll 0% 0%">O. Esen, S. Sütlü, (2018).
Matched pairs of discrete dynamical systems. arXiv preprint
arXiv:1809.00521. </span><span style="font-family:"Times New Roman","serif""><span></span></span></li><li class="MsoNormal" style="color:black;line-height:normal;margin:0cm 0cm 10pt;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-family:"Times New Roman","serif"">O. Esen, S. Sütlü, (2017), Lagrangian Dynamics on
Matched Pairs, Journal of Geometry and Physics 111C (2017) pp.
142-157.<span></span></span></li><li class="MsoNormal" style="color:black;line-height:normal;margin:0cm 0cm 10pt;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-family:"Times New Roman","serif"">O. Esen, S. Sütlü, (2016), Hamiltonian dynamics
on matched pairs, International Journal of Geometric Methods in Modern
Physics, Vol. 13, No. 10 (2016) 1650128 (24 pages)<span></span></span></li></ul>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-family:"Times New Roman","serif";color:black"><span> </span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-family:"Times New Roman","serif";color:black"><u>Tarih: 10 Ekim 2019 Perşembe,
16:00</u><span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-family:"Times New Roman","serif";color:black">Yer: Matematik Bölümü
Seminer Odası<span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-family:"Times New Roman","serif";color:black"><span> </span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><i><span style="font-family:"Times New Roman","serif";color:black">Seminerde görüşmek
dileğiyle,</span></i><font color="#888888"><span style="font-family:"Times New Roman","serif";color:black"><span></span></span></font></p><font color="#888888">
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-family:"Times New Roman","serif";color:black"><span> </span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><i><span style="font-family:"Times New Roman","serif";color:black">Fatma Altunbulak Aksu</span></i><span style="font-family:"Times New Roman","serif";color:black"><span></span></span></p>
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