具有随机输运的非完整系统的动力学
Dynamics of non-holonomic systems with stochastic transport
摘要：
本文提出了一种变分方法，用于处理观测不确定性和/或计算模型误差作为随机输运的动力系统的作用原理下的非完整约束。为此，我们推导、分析和数值研究了不平衡球在重力作用下沿随机路径滚动的例子，我们的方法使用Hamilton-Pontryagin变分原理，并受随机滚动条件的约束，我们证明了它与相应的随机Lagrange-d 'Alembert原理是等价的。在滚动球的示例中，随机性表示滚动的角速度的计算模拟中的观测和/或误差的不确定性。从解析和数值两方面研究了随机性对确定性守恒量的影响。我们的方法适用于各种各样的随机，非完整约束系统，因为它保留了从变分原理继承的数学性质。关键词：非完整约束，随机动力学，输运噪声。
英文摘要：
This paper formulates a variational approach for treating observational uncertainty and/or computational model errors as stochastic transport in dynamical systems governed by action principles under nonholonomic constraints. For this purpose, we derive, analyze and numerically study the example of an unbalanced spherical ball rolling under gravity along a stochastic path. Our approach uses the Hamilton-Pontryagin variational principle, constrained by a stochastic rolling condition, which we show is equivalent to the corresponding stochastic Lagrange-d'Alembert principle. In the example of the rolling ball, the stochasticity represents uncertainty in the observation and/or error in the computational simulation of the angular velocity of rolling. The influence of the stochasticity on the deterministically conserved quantities is investigated both analytically and numerically. Our approach applies to a wide variety of stochastic, nonholonomically constrained systems, because it preserves the mathematical properties inherited from the variational principle. Keywords: Nonholonomic constraints, Stochastic dynamics, Transport noise.
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