构造具有力的等价保持Dirac变分积分器
Constructing equivalence-preserving Dirac variational integrators with forces
AI总结：
本文研究了构造具有力的Dirac变分积分器，通过保持几何结构提高数值积分的准确性并减少长时间误差，适用于互联机械系统。
摘要：
机械系统动力学具有内在的几何结构，保持这些结构在数值积分中可以提高定性精度并减少长时间误差。对于单个机械系统，可以通过采用变分积分器构造来保持结构。这种构造已被推广到更复杂的系统，包括力或约束以及Dirac力学的设定。变分积分器最近被应用于互联系统，在Parks和Leok（2017）中被应用，这些系统是实际有用的机械系统的重要类别，其描述在Jacobs和Yoshimura（2014）中被阐明。由于这些互联系统被建模为具有连接力的子系统集合，我们重新审视了一些强制变分积分器的性质。特别是，我们推导出一类具有力的Dirac变分积分器，其保持性质在将变分积分器应用于互联Dirac系统的离散化时至关重要。最后，我们基于这些发现讨论了正在进行和未来的研究。
英文摘要：
The dynamical motion of mechanical systems possesses underlying geometric structures, and preserving these structures in numerical integration improves the qualitative accuracy and reduces the long-time error of the simulation. For a single mechanical system, structure preservation can be achieved by adopting the variational integrator construction. This construction has been generalized to more complex systems involving forces or constraints as well as to the setting of Dirac mechanics. Variational integrators have recently been applied to interconnected systems in Parks and Leok (2017), which are an important class of practically useful mechanical systems whose description in terms of Dirac structures and Dirac mechanical systems was elucidated in Jacobs and Yoshimura (2014). Since these interconnected systems are modeled as a collection of subsystems with forces of interconnection, we revisit some of the properties of forced variational integrators. In particular, we derive a class of Dirac variational integrators with forces that exhibit preservation properties that are critical when applying variational integrators to the discretization of interconnected Dirac systems. We close with a discussion of ongoing and future research based on these findings.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
