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<div><span style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0)">各位</span></div>
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<div>立命館大学数理科学科に所属しております多羅間大輔と申します．</div>
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<div>多羅間 大輔</div>
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<div>記</div>
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<div><<立命館大学幾何学セミナー>></div>
<div>日時：2022年1月31日（月） 16:30～18:00</div>
<div>タイトル： A geometric approach to stochastic extensions of nonholonomic constraints</div>
<div>講演者： François Gay-Balmaz（CNRS - LMD - Ecole Normale <span>Supérieure</span>）</div>
<div>アブストラクト：</div>
<div>We propose several stochastic extensions of nonholonomic constraints for mechanical systems and study the effects on the dynamics and on the conservation laws. Our approach relies on a stochastic extension of the Lagrange-d'Alembert framework. The mechanical
system we focus on is the example of a Routh sphere, i.e., a rolling unbalanced ball on the plane. We interpret the noise in the constraint as either a stochastic motion of the plane, random slip or roughness of the surface. Without the noise, this system
possesses three integrals of motion: energy, Jellet and Routh. Depending on the nature of noise in the constraint, we show that either energy, or Jellet, or both integrals can be conserved, with probability 1. We also present some exact solutions for particular
types of motion in terms of stochastic integrals.
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Inspired by this example, we then consider two different ways of including stochasticity in nonholonomic systems. We show that when the noise preserves the linearity of the constraints, then energy is. preserved. For other types of noise in the constraint,
e.g., in the case of an affine noise, the energy is not conserved. This approach is illustrated with a class of Lagrangian mechanical systems on Lie groups, with constraints of "rolling ball type". We conclude with numerical simulations illustrating our theories,
and some pedagogical examples of noise in constraints for other nonholonomic systems popular in the literature, such as the nonholonomic particle, the rolling disk and the Chaplygin sleigh.</div>
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<div><a href="https://ritsumei-ac-jp.zoom.us/meeting/register/tJEtd--srzktHtXaNonigAyY3oupOwhcZRLm" id="LPNoLPOWALinkPreview">https://ritsumei-ac-jp.zoom.us/meeting/register/tJEtd--srzktHtXaNonigAyY3oupOwhcZRLm</a></div>
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<div>問い合わせ先：立命館大学理工学部数理科学科</div>
<div> 多羅間 大輔</div>
<div> dtarama [at] fc.ritsumei.ac.jp</div>
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<div>************************************</div>
<div>Daisuke TARAMA</div>
<div>Department of Mathematical Sciences</div>
<div>Ritsumeikan University</div>
<div>Address: 1-1-1 Nojihigashi,</div>
<div>Kusatsu, Shiga, 525-8577, Japan</div>
<div>Office: West Wing (WW) 606</div>
<div>E-mail: dtarama [at] fc.ritsumei.ac.jp</div>
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