发表机构
TU Berlin; University of Groningen（柏林工业大学; 格罗宁根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文推导比较非线性耗散哈密顿与端口哈密顿微分代数方程系统的不同表示，结合几何代数结构处理约束，阐释于受约束力学系统，讨论约束转换并研究极大单调结构以纳入耗散。
AI 中文摘要
本文推导并比较了非线性耗散哈密顿系统与端口哈密顿（pH）微分代数方程（DAE）系统的不同表示形式。从全局几何与代数视角出发，包括奇异拉格朗日结构、狄拉克结构以及莫尔斯族及其斜对偶结构，将约束纳入模型中。通过含运动学与几何约束的受约束力学系统具体阐释所得结果，研究了不同表示形式间的关系，尤其讨论了拉格朗日代数约束与狄拉克代数约束间的相互转换。为纳入耗散，还研究了极大单调结构。
英文摘要
Different representations of nonlinear dissipative Hamiltonian and port-Hamiltonian (pH) differential-algebraic equations (DAE) systems are derived and compared. Using global geometric and algebraic points of view, including singular Lagrange and Dirac structures, as well as Morse families and their skew counterparts, constraints are incorporated in the models. The results are illustrated specifically with constrained mechanical systems using kinematic and geometric constraints. The relation between the different representations is studied and in particular the conversion of Lagrange into Dirac algebraic constraints and vice versa is discussed. To incorporate dissipation also maximally monotone structures are studied.
