非完整系统在Gauss白噪声下的扰动

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Gauss White Noise Perturbations of Nonholonomic Mechanical Systems

摘要: 本文研究非完整系统在Gauss白噪声下的扰动,证明解过程的一次矩方程与无扰动情形下的方程一致,二次矩方程不含ε项,但包含ε²项,从而得出两个命题.最后,举例说明结果的应用.
- 非完整系统 /
- 白噪声 /
- 随机微分方程
Abstract: The perturbations of nonholonomic mechanical systems under the Gauss white noises are studied in this paper. It is proved that the differential equations of the first-order moments of the solution process coincide with the corresponding equations in the non-perturbational case, and that there are ε²-terms but no ε-terms in the differential equations of the second-order moments. Two propositions are obtained. Finally, an example is given to illustrate the application of the results.
- nonholonomic systems /
- white noises /
- random differential equations

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