06/09/2016, 15:40 — 16:20 — Amphitheatre Pa2, Mathematics Building
Gláucio Terra, IME, Universidade de São Paulo

Vakonomic vs Nonholonomic Mechanics Revisited

The purpose of this talk is to present conditions under which vakonomic and nonholonomic mechanics for linearly constrained mechanical systems coincide. The main result states that, if the vakonomic vector field is tangent to the Whitney sum $\mathcal{D} \oplus (\mathcal{D}^0)^{(1)}$, where $\mathcal{D}$ is the constraint distribution and $(\mathcal{D}^0)^{(1)}$ is the first derived system of the annihilator $\mathcal{D}^0 \subset T^*M$ of $\mathcal{D}$ in the cotangent bundle of the configuration manifold $M$, then the the projection on $\mathcal{D}$ of the vakonomic trajectories with initial condition in this Whitney sum coincide with the nonholonomic trajectories.