3 citations · 3 across the 4 of their papers we have counts for
4 papers
High-order symplectic Lie group methods on using the polar decomposition
Xuefeng Shen, Khoa Tran, Melvin Leok
A variational integrator of arbitrarily high-order on the special orthogonal group is constructed using the polar decomposition and the constrained Galerkin method. It has…
Geometric Symmetry Reduction of the Unobservable Subspace for Kalman Filtering
Xuefeng Shen, Melvin Leok
In this article, we consider the implications of unobservable subspaces in the construction of a Kalman filter. In particular, we consider dynamical systems which are invariant wit…
Lie group variational integrators for rigid body problems using quaternions
Xuefeng Shen, Melvin Leok
Rigid body dynamics on the rotation group have typically been represented in terms of rotation matrices, unit quaternions, or local coordinates, such as Euler angles. Due to the co…
Geometric Exponential Integrators
Xuefeng Shen, Melvin Leok
In this paper, we consider exponential integrators for semilinear Poisson systems. Two types of exponential integrators are constructed, one preserves the Poisson structure, and th…