Variational integrators for forced Birkhoffian systems

详细信息    查看全文

• 作者：Xinlei Kong ; Huibin Wu ; Fengxiang Mei
• 关键词：Variational integrator ; Pfaff&ndash ; Birkhoff&ndash ; D&rsquo ; Alembert principle ; Discrete forced Birkhoffian equations
• 刊名：Applied Mathematics and Computation
• 出版年：1 December, 2013
• 年：2013
• 卷：225
• 期：Complete
• 页码：326-332
• 全文大小：393 K

文摘

In this letter, we first extend the Pfaff-Birkhoff principle to include forces and obtain the Pfaff-Birkhoff-D鈥橝lembert principle consequently. Well then motions of forced Birkhoffian systems coincide with extremals of the modified principle. Subsequently, compared with the continuous case, the discrete forced Birkhoffian equations are constructed by discretizing the Pfaff-Birkhoff-D鈥橝lembert principle. Considered as algorithms, the discrete equations have good numerical behavior in terms of getting the correct amounts by which the energy changes over the integration process, demonstrated by the given example.