In the theory of discrete mechanics, discrete-time numerical approximations of a physical principle, such as Hamilton's principle, are used to derive a set of governing difference equations with solutions approximately sampling the continuous-time system evolution. These difference equations are referred to as variational integrators. Extensive study of variational integrators has revealed many unique numerical properties. They are symplectic, they have stable long-time energy behavior, they perfectly satisfy holonomic constraints, they accurately compute statistical quantities, and they conserve, or nearly conserve, symmetries of system dynamics. These properties have made variational integrators an attractive option for numerical simulation in a variety of fields, but their use in real-world embedded systems has been limited to a small number of instances. However, these properties suggest potential benefits in standard control and estimation routines applied to embedded systems. Investigating these effects is the primary focus of this work.
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