标题： 非完整力学的拉格朗日神经网络 显示英文标题

标题： Lagrangian neural networks for nonholonomic mechanics

摘要： 拉格朗日神经网络（LNNs）是一种处理物理系统（尤其是受守恒定律支配的系统）的强大工具。LNNs 可以参数化系统的拉格朗日函数，从而预测几乎保持能量守恒的轨迹。 这些技术在无约束系统以及具有完整约束的系统中均被证明是有效的。在本研究中，我们将 LNN 技术应用于具有非完整约束的机械系统。 我们通过一些具有非完整约束的经典例子测试了我们的方法，结果显示，将这些限制纳入神经网络的学习不仅提高了轨迹估计的准确性，还确保了对约束的遵守，并且与无约束的情况相比，表现出更好的能量行为。 显示英文摘要

摘要： Lagrangian Neural Networks (LNNs) are a powerful tool for addressing physical systems, particularly those governed by conservation laws. LNNs can parametrize the Lagrangian of a system to predict trajectories with nearly conserved energy. These techniques have proven effective in unconstrained systems as well as those with holonomic constraints. In this work, we adapt LNN techniques to mechanical systems with nonholonomic constraints. We test our approach on some well-known examples with nonholonomic constraints, showing that incorporating these restrictions into the neural network's learning improves not only trajectory estimation accuracy but also ensures adherence to constraints and exhibits better energy behavior compared to the unconstrained counterpart.