Event-Selected Vector Field Discontinuities Yield Piecewise-Differentiable Flows
Event-Selected Vector Field Discontinuities Yield Piecewise-Differentiable Flows
复制标题
事件选择的向量场不连续性产生分段可微流
DOI：
--
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发表时间：
2014
影响因子：
2.1
通讯作者：
Shai Revzen
中科院分区：
文献类型：
--
作者：
Samuel A. Burden;S. Sastry;D. Koditschek;Shai Revzen
我们研究一类由多足动物运动引起我们注意的不连续向量场。这样的矢量场不仅出现在生物力学中，而且出现在机器人学、神经科学和电气工程中，仅举几个应用领域。在（i）向量场的不连续性局部地局限于有限个光滑子流形和（ii）向量场在适当的意义上横截于这些曲面的条件下，已知向量场产生一个定义良好的Lipschitz连续流。我们扩展这些结果表明，这个流是分段-可微的，所以它承认一阶近似（称为Bouligand衍生物）是分段-线性和连续的每一点。我们利用这种一阶近似来推断分段可微的影响地图（包括庞加莱映射的周期轨道）的存在性，表明流是局部共轭（通过分段可微同胚）的f…
We study a class of discontinuous vector fields brought to our attention by multilegged animal locomotion. Such vector fields arise not only in biomechanics, but also in robotics, neuroscience, and electrical engineering, to name a few domains of application. Under the conditions that (i) the vector field's discontinuities are locally confined to a finite number of smooth submanifolds and (ii) the vector field is transverse to these surfaces in an appropriate sense, it is known that the vector field yields a well--defined flow that is Lipschitz continuous. We extend these results by showing this flow is piecewise--differentiable, so that it admits a first--order approximation (known as a Bouligand derivative) that is piecewise--linear and continuous at every point. We exploit this first--order approximation to infer existence of piecewise--differentiable impact maps (including Poincare maps for periodic orbits), show that the flow is locally conjugate (via a piecewise--differentiable homeomorphism) to a f...
影响因子：
56.9
作者：
SCHONER, G;KELSO, JAS
通讯作者：
KELSO, JAS
影响因子：
2.1
作者：
Jeffrey, Mike R.
通讯作者：
Jeffrey, Mike R.