The Boltzmann-Hamel equations for optimal control

@article{Maruskin2007TheBE,
  title={The Boltzmann-Hamel equations for optimal control},
  author={Jared M. Maruskin and Anthony M. Bloch},
  journal={2007 46th IEEE Conference on Decision and Control},
  year={2007},
  pages={554-559}
}
We introduce a fourth order version of the Boltzmann-Hamel equations, which yields a reduced set of equations for the kinematic and dynamic optimal control problems for mechanical systems with nonholonomic constraints. In particular, we will show the dynamic optimal control problem can be written as a minimal set of 4n - 2m first order differential equations of motion. 

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