吉村　浩明

掲載種別：研究論文（学術雑誌）

概要：We propose a variational formulation for the nonequilibrium thermodynamics of discrete open systems, i.e., discrete systems which can exchange mass and heat with the exterior. Our approach is based on a general variational formulation for systems with time-dependent nonlinear nonholonomic constraints and time-dependent Lagrangian. For discrete open systems, the time-dependent nonlinear constraint is associated with the rate of internal entropy production of the system. We show that this constraint on the solution curve systematically yields a constraint on the variations to be used in the action functional. The proposed variational formulation is intrinsic and provides the same structure for a wide class of discrete open systems. We illustrate our theory by presenting examples of open systems experiencing mechanical interactions, as well as internal diffusion, internal heat transfer, and their cross-effects. Our approach yields a systematic way to derive the complete evolution equations for the open systems, including the expression of the internal entropy production of the system, independently on its complexity. It might be especially useful for the study of the nonequilibrium thermodynamics of biophysical systems.

概要：In this paper, we develop variational integrators for the nonequilibrium thermodynamics of simple closed systems. These integrators are obtained by a discretization of the Lagrangian variational formulation of nonequilibrium thermodynamics developed in (Gay-Balmaz and Yoshimura 2017a J. Geom. Phys. part I 111 169–93; Gay-Balmaz and Yoshimura 2017b J. Geom. Phys. part II 111 194–212) and thus extend the variational integrators of Lagrangian mechanics, to include irreversible processes. In the continuous setting, we derive the structure preserving property of the flow of such systems. This property is an extension of the symplectic property of the flow of the Euler–Lagrange equations. In the discrete setting, we show that the discrete flow solution of our numerical scheme verifies a discrete version of this property. We also present the regularity conditions which ensure the existence of the discrete flow. We finally illustrate our discrete variational schemes with the implementation of an example of a simple and closed system.

ISSN：00222488

概要：© 2018 Author(s). Dirac structures are geometric objects that generalize both Poisson structures and presymplectic structures on manifolds. They naturally appear in the formulation of constrained mechanical systems. In this paper, we show that the evolution equations for nonequilibrium thermodynamics admit an intrinsic formulation in terms of Dirac structures, both on the Lagrangian and the Hamiltonian settings. In the absence of irreversible processes, these Dirac structures reduce to canonical Dirac structures associated with canonical symplectic forms on phase spaces. Our geometric formulation of nonequilibrium thermodynamic thus consistently extends the geometric formulation of mechanics, to which it reduces in the absence of irreversible processes. The Dirac structures are associated with the variational formulation of nonequilibrium thermodynamics developed in the work of Gay-Balmaz and Yoshimura, J. Geom. Phys. 111, 169-193 (2017a) and are induced from a nonlinear nonholonomic constraint given by the expression of the entropy production of the system.

掲載種別：研究論文（国際会議プロシーディングス）

ISSN：02731177

概要：© 2017 COSPAR In this paper, we show a low energy Earth–Moon transfer in the context of the Sun–Earth–Moon–spacecraft 4-body system. We consider the 4-body system as the coupled system of the Sun–Earth–spacecraft 3-body system perturbed by the Moon (which we call the Moon-perturbed system) and the Earth–Moon–spacecraft 3-body system perturbed by the Sun (which we call the Sun-perturbed system). In both perturbed systems, analogs of the stable and unstable manifolds are computed numeric ally by using the notion of Lagrangian coherent structures, wherein the stable and unstable manifolds play the role of separating orbits into transit and non-transit orbits. We obtain a family of non-transit orbits departing from a low Earth orbit in the Moon-perturbed system, and a family of transit orbits arriving into a low lunar orbit in the Sun-perturbed system. Finally, we show that we can construct a low energy transfer from the Earth to the Moon by choosing appropriate trajectories from both families and patching these trajectories with a maneuver.

ISSN：03930440

概要：© 2016 Elsevier B.V.In this paper, we present a Lagrangian variational formulation for nonequilibrium thermodynamics. This formulation is an extension of Hamilton's principle of classical mechanics that allows the inclusion of irreversible phenomena. The irreversibility is encoded into a nonlinear phenomenological constraint given by the expression of the entropy production associated to all the irreversible processes involved. From a mathematical point of view, our variational formulation may be regarded as a generalization to nonequilibrium thermodynamics of the Lagrange–d'Alembert principle used in nonlinear nonholonomic mechanics, where the conventional Lagrange–d'Alembert principle cannot be applied since the nonlinear phenomenological constraint and its associated variational constraint must be treated separately. In our approach, to deal with the nonlinear nonholonomic constraint, we introduce a variable called the thermodynamic displacement associated to each irreversible process. This allows us to systematically define the corresponding variational constraint. In Part I, our variational theory is illustrated with various examples of discrete systems such as mechanical systems with friction, matter transfer, electric circuits, chemical reactions, and diffusion across membranes. In Part II of the present paper, we will extend our variational formulation of discrete systems to the case of continuum systems.

ISSN：03930440

概要：© 2016 Elsevier B.V.Part I of this paper introduced a Lagrangian variational formulation for nonequilibrium thermodynamics of discrete systems. This variational formulation extends Hamilton's principle to allow the inclusion of irreversible processes in the dynamics. The irreversibility is encoded into a nonlinear nonholonomic constraint given by the expression of entropy production associated to all the irreversible processes involved. In Part II, we develop this formulation for the case of continuum systems by extending the setting of Part I to infinite dimensional nonholonomic Lagrangian systems. The variational formulation is naturally expressed in the material representation, while its spatial version is obtained via a nonholonomic Lagrangian reduction by symmetry. The theory is illustrated with the examples of a viscous heat conducting fluid and its multicomponent extension including chemical reactions and mass transfer.

掲載種別：研究論文（国際会議プロシーディングス）

ISSN：03930440

概要：© 2016 Elsevier B.V.In this paper, we make a generalization of Routh's reduction method for Lagrangian systems with symmetry to the case where not any regularity condition is imposed on the Lagrangian. First, we show how implicit Lagrange-Routh equations can be obtained from the Hamilton-Pontryagin principle, by making use of an anholonomic frame, and how these equations can be reduced. To do this, we keep the momentum constraint implicit throughout and we make use of a Routhian function defined on a certain submanifold of the Pontryagin bundle. Then, we show how the reduced implicit Lagrange-Routh equations can be described in the context of dynamical systems associated to Dirac structures, in which we fully utilize a symmetry reduction procedure for implicit Hamiltonian systems with symmetry.

掲載種別：研究論文（国際会議プロシーディングス）

掲載種別：研究論文（国際会議プロシーディングス）

掲載種別：研究論文（国際会議プロシーディングス）

掲載種別：研究論文（国際会議プロシーディングス）

ISSN：09189238

概要：本論文では,太陽-地球-月-宇宙機からなる制限4体系を,太陽-地球-宇宙機系と地球-月-宇宙機系の2つの制限3体系を結合したモデルを用いて,地球周回低軌道および月周回低軌道を境界条件として与える月遷移軌道の設計を行う.そのために,太陽-地球-宇宙機系では,地球近傍のチューブ(不変多様体)の構造を調べることで地球周回低軌道を離れる出発軌道を提案し,地球-月-宇宙機系においては,月近傍のチューブを調査することによって,月周回低軌道に輸送される到着軌道を見出す.それぞれの系において導出した軌道が接続点で滑らかにつながるように月遷移軌道を設計する.最後に,必要となるΔVについて他の手法と比較を行い,本論文による軌道の有効性を示す.

ISSN：03930440

概要：© 2015 Published by Elsevier B.V. In this paper, we explore dynamics of the nonholonomic system called vakonomic mechanics in the context of Lagrange-Dirac dynamical systems using a Dirac structure and its associated Hamilton-Pontryagin variational principle. We first show the link between vakonomic mechanics and nonholonomic mechanics from the viewpoints of Dirac structures as well as Lagrangian submanifolds. Namely, we clarify that Lagrangian submanifold theory cannot represent nonholonomic mechanics properly, but vakonomic mechanics instead. Second, in order to represent vakonomic mechanics, we employ the space TQ×V*, where a vakonomic Lagrangian is defined from a given Lagrangian (possibly degenerate) subject to nonholonomic constraints. Then, we show how implicit vakonomic Euler-Lagrange equations can be formulated by the Hamilton-Pontryagin variational principle for the vakonomic Lagrangian on the extended Pontryagin bundle (TQ⊕T*Q)×V*. Associated with this variational principle, we establish a Dirac structure on (TQ⊕T*Q)×V* in order to define an intrinsic vakonomic Lagrange-Dirac system. Furthermore, we also establish another construction for the vakonomic Lagrange-Dirac system using a Dirac structure on T*Q×V*, where we introduce a vakonomic Dirac differential. Finally, we illustrate our theory of vakonomic Lagrange-Dirac systems by some examples such as the vakonomic skate and the vertical rolling coin.

ISSN：0196-8858

概要：This paper develops the theory of Dirac reduction by symmetry for nonholonomic systems on Lie groups with broken symmetry. The reduction is carried out for the Dirac structures, as well as for the associated Lagrange–Dirac and Hamilton–Dirac dynamical systems. This reduction procedure is accompanied by reduction of the associated variational structures on both Lagrangian and Hamiltonian sides. The reduced dynamical systems obtained are called the implicit Euler–Poincaré–Suslov equations with advected parameters and the implicit Lie–Poisson–Suslov equations with advected parameters. The theory is illustrated with the help of finite and infinite dimensional examples. It is shown that equations of motion for second order Rivlin–Ericksen fluids can be formulated as an infinite dimensional nonholonomic system in the framework of the present paper.

掲載種別：研究論文（国際会議プロシーディングス）

ISSN：00214728

ISSN：1941-4889

概要：Many mechanical systems are large and complex, despite being composed of simple subsystems. In order to understand such large systems it is natural to tear the system into these subsystems. Conversely we must understand how to invert this tearing. In other words, we must understand interconnection. Such an understanding has already successfully understood in the context of Hamiltonian systems on vector spaces via the port-Hamiltonian systems program. In port-Hamiltonian systems theory, interconnection is achieved through the identification of shared variables, whereupon the notion of composition of Dirac structures allows one to interconnect two systems. In this paper we seek to extend the port-Hamiltonian systems program to Lagrangian systems on manifolds and extend the notion of composition of Dirac structures appropriately. In particular, we will interconnect Lagrange-Dirac systems by modifying the respective Dirac structures of the involved subsystems. We define the interconnection of Dirac structures via an interaction Dirac structure and a tensor product of Dirac structures. We will show how the dynamics of the interconnected system is formulated as a function of the subsystems, and we will elucidate the associated variational principles. We will then illustrate how this theory extends the theory of port-Hamiltonian systems and the notion of composition of Dirac structures to manifolds with couplings which do not require the identification of shared variables. Lastly, we will close with some examples: a mass-spring mechanical systems, an electric circuit, and a nonholonomic mechanical system.

ISSN：1348-0693

概要：For the sake of spacecraft mission design, it is indispensable to develop a low energy transfer of spacecrafts using very little fuel for interplanetary transport network. The Planar Circular Restricted Three-Body Problem (PCR3BP) has been a fundamental tool for the analysis \of such a space mission design. In this paper, we explore stable and unstable invariant manifolds associated with the collinear Lagrange points L1, L2 of the PCR3BP, in which geometric structures of the invariant manifolds are clarified on a Poincar\'a5'e section. Further, we compute the Finite Time Lyapunov Exponent fields (FTLE fields) to obtain Lagrangian Coherent Structures (LCS) as the ridges of the FTLE fields. In particular, we compare the LCS with the invariant manifolds on the Poincaré section from the viewpoint of the numerical integration times.

ISSN：1342-5668

概要：For the design of spacecraft transfer orbits in the Earth-Moon system, we need to model the dynamics in the context of the Planar Elliptic Restricted Three-Body Problem (PER3BP) since it has a non-negligible eccentricity. In this paper, we investigate invariant manifolds of the PER3BP by analyzing Lagrangian Coherent Structures (LCS). In particular, we show that the transfer orbits from the exterior realm to Moon can be developed by employing the geometric characteristics of the LCS obtained by long time numerical integrations.

掲載種別：研究論文（国際会議プロシーディングス）

掲載種別：研究論文（学術雑誌）

概要：惑星間を航行する宇宙機の力学モデルは，平面円制限三体問題として考えることができる．２つの天体と直線上にあるラグランジュ点近傍においてリアプノフ軌 道と呼ばれる不安定な周期軌道からはチューブと呼ばれる不変多様体が伸びている．このチューブを利用することで，低エネルギーかつ安定な軌道の設計を行う事ができるが，チューブはセパトリクス構造を有するために，従来のモノドロミー行列を用いた解析には数値精度の面で不安が残る．そこで，本研究では，ベクトル場の伸縮を計る有限時間リアプノフ指数を用いてチューブを解析し，従来のアプローチを補完することで平面円制限三体問題における不変多様体の構造を明らかにする．

掲載種別：研究論文（学術雑誌）

概要：The paper presents a modeling method of flexible multibody dynamics in the context of implicit Lagrangian systems. The main idea is based on a Diakoptical method originally developed by Kron, which reticulates required kinematical and dynamical relations into separate ones and then incorporate them into an interconnection of implicit Lagrangian systems. By using the idea, we first show how a flexible beam attached to a rigid base undergoing a large overall motion can be modeled as an interconnected implicit Lagrangian system, in which geometrically nonlinear couplings between flexible deformations and large overall motions are incorporated into a nonlinear finite element model. Lastly, some numerical results are shown in comparison with the model developed by Simo and Vu-Quoc.

ISSN：1880-2818

掲載種別：研究論文（学術雑誌）

掲載種別：研究論文（国際会議プロシーディングス）

掲載種別：研究論文（国際会議プロシーディングス）

概要：The exploration of cavitation bubbles has been one of the most important challenging research problems in fluid dynamics. Much effort has been done to elucidate how bubbles may rebound and shrink from the viewpoint of macroscopic level. However, the bubble nucleation and collapse have not been fully clarified since they must be essentially microscopic phenomena. Therefore, it is indispensable to study bubble dynamics from the microscopic viewpoint of molecular dynamics. In this paper, we will show the MD simulation of bubble dynamics using Lennard-Jones particles and soft-core particles as non-condensable gas, and then we will illustrate generation of a single bubble by repulsive force. We will also show how the single bubble can shrink and collapse for the cases with and without non-condensable gas in the bubble.

概要：We show the variational formulation of the Rayleigh-Plesset equation for single bubble dynamics in static water by the Hamilton-Pontryagin principle. Then, we illustrate the bifurcation phenomena associated to an amplitude of the bubble radius response as to the amplitude of the input pressure under forced oscillating pressure at constant temperature. Lastly, we show that there exists a stable state of the amplitude of bubble radius under the forced pressure with higher frequencies.

ISSN：0393-0440

概要：　キャビテーションは流体機械の破壊をもたらす非定常現象として良 くしられているが，最近では，マイクロバブルに見られるように医 療などへの応用も注目されている．このようなキャビテーションの 初生は，気泡核の急激な成長と崩壊に起因すると考えられている が，未だ十分に解明されたとは言えない．そこで，本研究では，静 止流体中における単一気泡のダイナミクスを表すレイリー・プリ セット方程式を用いて，気泡の運動に現れる非線形現象を理論，数 値計算の両面から行うことを目的とする．
　まず，振動圧力場における等温状態での気泡半径の振動を数値計 算し，それが振幅の増加に伴って，周期倍分岐を繰り返しカオス的 状態に至ることを，分岐図を描くことによって示す．また，その分 岐図が，周波数や初期気泡半径の変化によってどのように変化する かを示す．次に，振動圧力場において振動していた気泡半径が，高 周波の振動圧力場においては，初期気泡半径に収束することを数値 計算によって示し，微小な気泡が安定に存在することを示す．

概要：1993年，探査衛星ガリレオによって小惑星「イダ」と「ダクティル」のペアが発見されて以来，小惑星ペアを含む人工衛星の軌道と安定性の解析が重要な技術的課題となっている．本研究では，特に，小惑星ペアの運動に焦点を絞り，余接バンドル簡約化の手法を用いて小惑星ペアの相対平衡を求める．その上で，エネルギー・運動量法による相対平衡に関する安定領域を明らかにする．

概要：海洋探査や海中環境調査の観点から魚ロボットや潜水艇の開発が盛んになっているが，水中を泳ぐ魚の推進メカニズムの理解には，工学ではあまり馴染みのないリー群や主バンドルといった幾何学的概念を用いることが不可欠である．本論文では，魚の推進メカニズムを理解するための物理モデルとして，ジョイントで接続された３つの剛体からなる２次元のマルチボディシステムを考え，完全流体中の魚の運動を特殊ユークリッド群による作用及びラグランジュ簡約を用いて定式化し，主バンドル上の接続を用いて表現する．その上で，魚の泳ぎを数値計算によって再現する．

掲載種別：研究論文（国際会議プロシーディングス）

掲載種別：研究論文（国際会議プロシーディングス）

概要：We develop the Hamilton‐Pontryagin principle for Lagrangians with advective parameters, which yields an implicit analogue of Euler‐Poincaré equations with advective parameters. Then, we derive the reduced Hamilton‐Pontryagin principle and illustrate it with the example of incompressible ideal fluids, where the configuration space is given by the group of (volume preserving) diffeomorphisms. Incorporating pressure and momentum densities as Lagrange multipliers into the Hamilton‐Pontryagin principle, we finally show that the dynamics of incompressible ideal fluids can be effectively formulated in the context of implicit Euler‐Poincaré equations.

掲載種別：研究論文（国際会議プロシーディングス）

ISSN：09135685

概要：相反な非線形回路システムの内部接続構造とBrayton-Moser方程式について述べる.特に,その応用として,神経膜の数理モデルの一つであるFitzHugh-Nagumoモデルを取り上げ,システムの接続構造の性質から混合ポテンシャルが存在することを示し,その上で,Brayton-Moser方程式に基づく定式化を行う.また,数値解析によって膜電位ダイナミクスの数値シミュレーションを行う.

ISSN：02859947

ISSN：18802818

掲載種別：研究論文（国際会議プロシーディングス）

掲載種別：研究論文（国際会議プロシーディングス）

掲載種別：研究論文（国際会議プロシーディングス）

掲載種別：研究論文（国際会議プロシーディングス）

掲載種別：研究論文（国際会議プロシーディングス）

掲載種別：研究論文（国際会議プロシーディングス）

概要：The authors’ recent paper in Reports in Mathematical Physics develops Dirac reduction for cotangent bundles of Lie groups, which is called Lie– Dirac reduction. This procedure simultaneously includes Lagrangian, Hamiltonian, and a variational view of reduction. The goal of the present paper is to generalize Lie–Dirac reduction to the case of a general configuration manifold; we refer to this as Dirac cotangent bundle reduction. This reduction procedure encompasses, in particular, a reduction theory for Hamiltonian as well as implicit Lagrangian systems, including the case of degenerate Lagrangians. First of all, we establish a reduction theory starting with the Hamilton- Pontryagin variational principle, which enables one to formulate an implicit analogue of the Lagrange-Poincar´e equations. To do this, we assume that a Lie group acts freely and properly on a configuration manifold, in which case there is an associated principal bundle and we choose a principal connection. Then, we develop a reduction theory for the canonical Dirac structure on the cotangent bundle to induce a gauged Dirac structure. Second, it is shown that by making use of the gauged Dirac structure, one obtains a reduction procedure for standard implicit Lagrangian systems, which is called Lagrange- Poincar´e-Dirac reduction. This procedure naturally induces the horizontal and vertical implicit Lagrange-Poincar´e equations, which are consistent with those derived from the reduced Hamilton-Pontryagin principle. Further, we develop the case in which a Hamiltonian is given (perhaps, but not necessarily, coming from a regular Lagrangian); namely, Hamilton-Poincar´e-Dirac reduction for the horizontal and vertical Hamilton-Poincar´e equations. We illustrate the reduction procedures by an example of a satellite with a rotor. The present work is done in a way that is consistent with, and may be viewed as a specialization of the larger context of Dirac reduction, which allows for Dirac reduction by stages. This is explored in a paper in preparation by Cendra, Marsden, Ratiu and Yoshimura.

掲載種別：研究論文（学術雑誌）

掲載種別：研究論文（国際会議プロシーディングス）

掲載種別：研究論文（学術雑誌）

掲載種別：研究論文（国際会議プロシーディングス）

掲載種別：研究論文（学術雑誌）

概要：This paper develops the notion of implicit Lagrangian systems and presents some of their basic properties in the context of Dirac structures. This setting includes degenerate Lagrangian systems and systems with both holonomic and nonholonomic constraints, as well as networks of Lagrangian mechanical systems. The definition of implicit Lagrangian systems with a configuration space $Q$ makes use of Dirac structures on $T^*Q$ that are induced from a constraint distribution on $Q$ as well as natural symplectomorphisms between the spaces $T^*TQ$, $TT^*Q$, and $T^*T^*Q$. Two illustrative examples are presented; the first is a nonholonomic system, namely a vertical disk rolling on a plane and the second is an L-C circuit, a degenerate Lagrangian system with holonomic constraints.

掲載種別：研究論文（学術雑誌）

概要：Part I of this paper introduced the notion of implicit Lagrangian systems and their geometric structure was explored in the context of Dirac structures. In this part, we develop the variational structure of implicit Lagrangian systems. Specifically, we show that the implicit Euler-Lagrange equations can be formulated using an extended variational principle of Hamilton called the Hamilton-Pontryagin principle. This vari- ational formulation incorporates, in a natural way, the generalized Legendre transfor- mation, which enables one to treat degenerate Lagrangian systems. The definition of this generalized Legendre transformation makes use of natural maps between iterated tangent and cotangent spaces. Then, we develop an extension of the classical Lagrange- d’Alembert principle called the Lagrange-d’Alembert-Pontryagin principle for implicit Lagrangian systems with constraints and external forces. A particularly interesting case is that of nonholonomic mechanical systems that can have both constraints and external forces. In addition, we define a constrained Dirac structure on the constraint momentum space, namely the image of the Legendre transformation (which, in the degenerate case, need not equal the whole cotangent bundle). We construct an im- plicit constrained Lagrangian system associated with this constrained Dirac structure by making use of an Ehresmann connection. Two examples, namely a vertical rolling disk on a plane and an L-C circuit are given to illustrate the results.

掲載種別：研究論文（国際会議プロシーディングス）

掲載種別：研究論文（国際会議プロシーディングス）

掲載種別：研究論文（国際会議プロシーディングス）

掲載種別：研究論文（国際会議プロシーディングス）

掲載種別：研究論文（国際会議プロシーディングス）

掲載種別：研究論文（国際会議プロシーディングス）

掲載種別：研究論文（学術雑誌）

掲載種別：研究論文（国際会議プロシーディングス）

掲載種別：研究論文（国際会議プロシーディングス）

掲載種別：研究論文（国際会議プロシーディングス）

掲載種別：研究論文（学術雑誌）

掲載種別：研究論文（国際会議プロシーディングス）

単行本（学術書）総ページ数：15担当ページ数：233-247

総ページ数：19担当ページ数：333-351

総ページ数：25担当ページ数：447-471ISBN：978-1-4613-7973-7

総ページ数：17担当ページ数：31-46ISBN：ISBN: 978-1-86094-058-3

国内会議口頭発表（一般）

国内会議

国内会議口頭発表（一般）

国際会議口頭発表（基調）開催地：Quebec

概要： In recent developments of modeling and analysis for physical systems such as multibody systems, electric circuits, chemical reactions, fluid systems and thermodynamic systems, much concern has been focused on how to systematically formulate the dynamics of such physical systems, in particular, concerning with multi-physical phenomena. To do this, it is essential to make a mathematical model of such a physical system by structuring in a unified way, so that the system can be regarded as an energetically interconnected system of constituent subsystems or interacting different physical systems. In classical mechanics, one can formulate the dynamics of unconstrained systems as Euler-Lagrange equations or Hamilton equations using variational principles, where these variational approaches are known to be consistent with symplectic structures on phase spaces. For the systems with nonholonomic constraints, the Lagrange-d’Alembert principle is associated with an induced Dirac structure on the phase space, which is a generalized notion of symplectic and Poisson structures, where the Dirac structure plays an essential role of the interconnection structure among energetic elements. In this talk, we first begin with the fundamental setting of the symplectic approach to Lagrangian and Hamiltonian systems and we consider the generalization to nonholonomic systems. In particular, we show the Dirac formulation of nonholonomic systems, in which we show that the Dirac structure represents the interconnection structure of various physical systems and also that how various physical systems such as nonholonomic mechanical systems, electric circuits, and rigid bodies with constraints can be regarded as an interconnected system in a unified way. Further, we develop the associated Dirac dynamical formulation for the systems together with the variational structure. Second, we study symmetry reduction called Lie-Dirac reduction, in which the configuration space is given by a Lie group and the dynamics can be represented by the implicit versions of Euler-Poincare equations and Lie-Poisson equations with constraints. We illustrate the theory with some examples of rigid bodies, multibody systems, etc. We also discuss the discrete variational principles to develop variational integrators which preserves the associated geometric structures along the flow map, together with some illustrative examples of molecular dynamics. Finally, we show some recent developments in nonequilibrium thermodynamics as a more general class of nonlinear nonholonomic systems, which can be also formulated in the context of the Dirac formulation together with the associated variational structures.

国際会議口頭発表（一般）開催地：Shijiazhuang

国際会議口頭発表（招待・特別）開催地：Beijing

国際会議口頭発表（一般）開催地：Taipei University

国際会議口頭発表（一般）開催地：Taipei University

国際会議口頭発表（一般）開催地：Anaheim

国際会議口頭発表（一般）開催地：Barcelona

国際会議口頭発表（一般）開催地：Barcelona

国際会議口頭発表（招待・特別）開催地：Technical University of Santa Maria

国際会議口頭発表（招待・特別）開催地：Technical University of Santa Maria

国内会議口頭発表（一般）

国内会議口頭発表（一般）

国際会議口頭発表（一般）開催地：OAXACA

国際会議口頭発表（一般）開催地：Oaxaca

国際会議口頭発表（一般）開催地：Snowbird

国際会議口頭発表（一般）開催地：Snowbird

国際会議口頭発表（基調）開催地：Kanazawa

開催地：Orlando

国際会議口頭発表（一般）開催地：Edmonton

国内会議口頭発表（一般）

セミナー開催地：尼崎

国内会議ポスター発表

国内会議ポスター発表

国内会議ポスター発表

国際会議口頭発表（一般）開催地：Snowbird

国際会議口頭発表（一般）開催地：Snowbird

国内会議口頭発表（一般）開催地：京都大学

国際会議口頭発表（一般）開催地：Tokyo

国際会議口頭発表（一般）開催地：Madrid

国際会議口頭発表（一般）開催地：Sanya

国内会議ポスター発表開催地：Taiwan National Tsing Hua University

国際会議口頭発表（一般）開催地：Valladolid

国際会議口頭発表（一般）開催地：Snowbird

国際会議口頭発表（一般）開催地：Ghent University

国際会議口頭発表（一般）開催地：University of Toronto

国際会議口頭発表（一般）開催地：University of Melbourne

国内会議セミナー開催地：Keio University

国際会議口頭発表（一般）開催地：Oberwolfach

講義等開催地：慶応義塾大学

セミナー開催地：慶応義塾大学

セミナー開催地：新潟大学

国際会議口頭発表（一般）開催地：Centro Atómico Bariloche

国内会議口頭発表（基調）開催地：東京コンファレンスセンター品川

国内会議ポスター発表開催地：CIRM, Liminy, France

セミナー開催地：京都大学

国内会議口頭発表（一般）開催地：慶応義塾大学

開催地：上智大学

国際会議口頭発表（一般）開催地：Waseda University

国際会議口頭発表（一般）開催地：Ghent University

国際会議口頭発表（一般）開催地：University of Manchester

講義等開催地：慶應義塾大学

口頭発表（招待・特別）開催地：北海道大学

国際会議口頭発表（一般）開催地：Waseda University

開催地：岐阜大学

開催地：名古屋

国際会議口頭発表（一般）開催地：Mathematical Institute at Oberwolfach, Germany

国内会議口頭発表（一般）開催地：琵琶湖コンファレンスセンター

国内会議口頭発表（招待・特別）開催地：神戸大学百年記念館

国際会議口頭発表（一般）開催地：Tokyo

開催地：京都大学数理解析研究所

講義等開催地：California Institute of Technology

国際会議口頭発表（一般）開催地：San Antonio

講義等開催地：California Institute of Technology

セミナー開催地：早稲田大学

開催地：Blacksburg

国際会議口頭発表（一般）開催地：California Institute of Technology

国内会議口頭発表（招待・特別）開催地：キャンパスプラザ京都

国内会議口頭発表（一般）開催地：京都大学数理解析研究所

国内会議セミナー開催地：早稲田大学数理科学科

国内会議口頭発表（招待・特別）開催地：東京都立科学技術大学

開催地：慶応大学数理科学科

国内会議講習開催地：ぱ・る・るプラザ京都

国内会議口頭発表（一般）開催地：京都大学数理解析研究所

国際会議口頭発表（一般）開催地：Erwin Schroedinger Institute, Vienna

国際会議口頭発表（一般）開催地：Shanghai

講義等開催地：筑波大学

講義等開催地：筑波大学

国内会議口頭発表（一般）開催地：琵琶湖コンファレンスセンター

国際会議口頭発表（一般）開催地：St. Petersburg

セミナー開催地：京都大学

国際会議口頭発表（一般）開催地：Chicago

国際会議口頭発表（一般）開催地：Blacksburg

セミナー開催地：Texas A & M University. College Station

国内会議口頭発表（一般）開催地：慶応義塾大学

国内会議口頭発表（一般）開催地：岐阜ホテルグランパレ

講習開催地：東京信濃町

開催地：Stanford University

国内会議口頭発表（招待・特別）開催地：神戸大学滝川記念学術交流会館

国内会議口頭発表（基調）