The Herglotz Principle and Vakonomic Dynamics

  title={The Herglotz Principle and Vakonomic Dynamics},
  author={Manuel de Le'on and Manuel Lainz and Miguel C. Mu{\~n}oz-Lecanda},
In this paper we study vakonomic dynamics on contact systems with nonlinear constraints. In order to obtain the dynamics, we consider a space of admisible paths, which are the ones tangent to a given submanifold. Then, we find the critical points of the Herglotz action on this space of paths. This dynamics can be also obtained through an extended Lagrangian, including Lagrange multiplier terms. This theory has important applications in optimal control theory for Herglotz control problems, in… 
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