发表机构
Rutgers University; Centre National de la Recherche Scientifique; Sorbonne Université（罗格斯大学; 法国国家科学研究中心; 索邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究刚性杆弹簧链的离散模型，刻画零能约束，区分旋转子与翻转子状态，给出收敛条件及连续统残差展开，并通过数值实验验证。核心贡献是建立离散模型与连续统方程的一致性理论。
AI 中文摘要
我们研究了一个由弹性弹簧耦合的刚性杆一维链的离散拉格朗日模型。我们刻画了其零能约束的几何结构，并区分了旋转子（spinner）与翻转子（flipper）两种状态。在图型假设下，选定的零能链在重新标度后收敛到自治常微分方程的轨迹。对于物理连杆，我们确定了一个简单的交替选择准则，在该准则下，链在旋转子状态中形成唯一的单调异宿族。在翻转子状态中，我们确定了约束集的拓扑结构及后继者的数量，但将全局分支选择留作开放问题。我们还推导了单分量和双分量的连续统残差展开式，区分了时间相关解的一致性与其收敛性。可复现的数值实验测试了选定的旋转子递推及其渐近乘子；对于具有光滑周期数据的简化单分量模型，它们分别恢复了前导和修正连续统方程的一阶和二阶差异。
英文摘要
We study a discrete Lagrangian model for a one-dimensional chain of rigid rods coupled by elastic springs. We characterize the geometry of its zero-energy constraint and distinguish the spinner and flipper regimes. Under graph-type hypotheses, selected zero-energy chains converge, after rescaling, to trajectories of an autonomous ordinary differential equation. For the physical linkage, we identify a simple alternating selection criterion under which chains form a unique monotone heteroclinic family in the spinner regime. In the flipper regime, we determine the topology of the constraint set and the number of successors, but leave global branch selection open. We also derive one- and two-component continuum residual expansions, distinguishing consistency from convergence of time-dependent solutions. Reproducible numerical experiments test the selected spinner recurrence and its asymptotic multiplier; for a simplified one-component model with smooth periodic data, they recover first- and second-order discrepancies for the leading and corrected continuum equations, respectively.
