Energy‐conserving integrations are widely used in long‐time simulations of mechanical systems because they exhibit excellent stability and conserve the discrete energy in conservative systems. However, in many applications, their errors of other quantities, for example, trajectory errors, are generally not bounded and increase with time. This article develops a parameter‐preadjusted energy‐conserving integration for rigid body dynamics in terms of convected‐based vectors. To this end, we introduce the modified inertia representation into the Hamiltonian description of the rigid body dynamics, which leads to a modified formulation of Hamilton's equations including an undetermined parameter γ. After that, the direct discretization of the modified Hamilton's equations and the constraints in terms of finite increments in time gives an energy‐conserving integration. Error estimation suggests that the value of γ has a great influence on the discretization errors of the Hamilton's equations. Therefore, a preadjusting stage at the beginning of the simulation is devised to optimize γ for minimizing the numerical error. Numerical results demonstrate that the PECI not only preserves the energy exactly, but also presents significant higher accuracy of trajectory errors. In particular, the PECI can achieve approximately periodic trajectory errors for long‐time simulations if γ is well preadjusted.

中文翻译：

---

根据对流基向量对刚体动力学进行参数调整的节能积分

节能积分被广泛用于机械系统的长期仿真中，因为它们具有出色的稳定性，并且可以节省保守系统中的离散能量。但是，在许多应用中，它们的其他数量的误差（例如轨迹误差）通常不受限制，并且会随时间增加。本文基于对流向量，为刚体动力学开发了一个参数调整的节能积分。为此，我们将修改后的惯性表示形式引入到刚体动力学的哈密顿量描述中，从而得出了哈密顿方程的修改公式，其中包括不确定的参数γ。此后，修改后的汉密尔顿方程的直接离散化和时间有限增量方面的约束给出了节能积分。误差估计表明，γ值对汉密尔顿方程的离散误差有很大的影响。因此，在仿真开始时设计了一个预调节阶段来优化γ，以最大程度地减小数值误差。数值结果表明，PECI不仅可以精确地保留能量，而且可以显着提高轨迹误差的准确性。特别是，如果对γ进行了很好的调整，则PECI可以在长期仿真中获得大约周期性的轨迹误差。