Uniqueness of Filippov Sliding Vector Field on the Intersection of Two Surfaces in R-3 and Implications for Stability of Periodic Orbits

作者：Dieci L; Elia C^*; Lopez L

来源：Journal of Nonlinear Science, 2015, 25(6): 1453-1471.

DOI：10.1007/s00332-015-9265-6

• Filippov convexification
• Orbital equivalence
• Periodic orbit
• Stability

In this paper, we consider the class of smooth sliding Filippov vector fields in on the intersection of two smooth surfaces: , where , and , , are smooth functions with linearly independent normals. Although, in general, there is no unique Filippov sliding vector field on , here we prove that-under natural conditions-all Filippov sliding vector fields are orbitally equivalent to . In other words, the aforementioned ambiguity has no meaningful dynamical impact. We also examine the implication of this result in the important case of a periodic orbit a portion of which slides on Sigma.

• 出版日期2015-12