Projects
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Stochastic geometrically exact beam: Continuous-time geometric principles and variational discretizations This work presents variational principles for the dynamics of the stochastic geometrically exact beam, in both continuous- and discrete-time settings. The resulting two structure-preserving stochastic geometric integrators are shown to be stochastic extensions of the well-known deterministic staggered leapfrog scheme for the wave equation, and also stochastic extensions of Yee's scheme for spatially one-dimensional computational electromagnetism. Numerical results are shown to demonstrate the effectiveness of the proposed approaches. |
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Variational Unscented Kalman Filter on Matrix Lie Groups This work presents proposes a family of computationally efficient unscented Kalman filters (UKF-Vs) for mechanical systems on matrix Lie groups. |