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In this paper, we consider the class of sliding Filippov vector fields in R^3 on\udthe intersection  of two smooth surfaces:  S= 1 \ 2, where S_i = {x : h_i(x) = 0},\udand h_i : R^3 -> R, i = 1, 2, are smooth functions with linearly independent normals.\udAlthough, in general, there is no unique Filippov sliding vector field on , here we\udprove that –under natural conditions– all Filippov sliding vector fields determine the\udsame solution trajectory on . In other words, the aforementioned ambiguity has no\udmeaningful impact. We also examine the implication of this result in the important case of a periodic orbit a portion of which slides on S

journal of nonlinear science

Uniqueness of Filippov Sliding Vector Field on the Intersection of Two Surfaces in $$\mathbb {R}^3$$ R 3 and Implications for Stability of Periodic Orbits