Quasistatic approximations for stiff second order differential equations
Quasistatic approximations for stiff second order differential equations
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DOI：
10.1016/j.apnum.2012.06.030
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发表时间：
2012-10
影响因子：
2.8
通讯作者：
Steffen Weber;M. Arnold;M. Valášek
中科院分区：
文献类型：
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作者：
Steffen Weber;M. Arnold;M. Valášek
二阶常微分方程中的刚性项由于高频振荡而导致计算时间过长。准静态近似通过忽略惯性力来消除多体系统动力学仿真中的这些高频解分量。在本文中，我们研究了这种方法的近似误差，从奇异摄动理论的经典结果。详细研究了多体动力学线性隐式二阶模型方程到一阶奇摄动常微分方程正则（半）显式形式的转化。数值试验的腿和地面之间的刚性接触力的步行移动的机器人的模型表明，计算时间可以减少到10倍，使用建议的准静态近似。
Stiff terms in second order ordinary differential equations may cause large computation time due to high frequency oscillations. Quasistatic approximations eliminate these high frequency solution components in the dynamical simulation of multibody systems by neglecting inertia forces. In the present paper, we study the approximation error of this approach using classical results from singular perturbation theory. The transformation of the linearly implicit second order model equations from multibody dynamics to the canonical (semi-)explicit form of first order singularly perturbed ordinary differential equations is studied in detail. Numerical tests for the model of a walking mobile robot with stiff contact forces between legs and ground show that the computation time may be reduced by a factor up to 10 using the proposed quasistatic approximation.