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- Term Paper
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Abstract
The study of vibrating systems, particularly those equipped with geometrically consistent tuned mass dampers (GTMDs), plays a crucial role in understanding structural behavior and resilience against external forces. This research delves into the challenging domain of estimating parameters and states of vibrating structures adorned with GTMDs with precision. The application of dynamical systems in contemporary engineering necessitates a sophisticated modeling approach, especially when dealing with the complexities of structures on Riemannian manifolds. This paper introduces Kalman filters as a foundational tool for parameter and state estimation on Riemannian manifolds, particularly within the context of Lie Algebra. The research aims to bridge existing gaps in the literature related to parameter and state estimation in the context of vibrating structures with GTMDs.
Figure 1: Trajectory of Chaotic Pendulum on SO(3) Manifold
