Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds
(with N. Harris McClamroch and Taeyoung Lee) Monograph published in the Interaction of Mechanics and Mathematics series (Springer).
Lie Group Variational Collision Integrators for a Class of Hybrid Systems
(with K. Tran), SIAM Applied Dynamical Systems, 24(2), 1622-1667, 2025.
Geometric Methods for Adjoint Systems
(with Brian Tran), Journal of Nonlinear Science, 34:25 (75 pages), 2024.
On properties of adjoint systems for evolutionary PDEs
(with B.K. Tran, B.S. Southworth), Journal of Nonlinear Science, 34:95 (39 pages), 2024.
A Variational Formulation of Accelerated Optimization on Riemannian Manifolds
(with V. Duruisseaux), SIAM Journal on Mathematics of Data Science, 4(2), 649-674, 2022.
Adaptive Hamiltonian Variational Integrators and Applications to Symplectic Accelerated Optimization
(with V. Duruisseaux, J. Schmitt), SIAM Journal on Scientific Computing, 43(4), A2949-A2980 (32 pages), 2021.
Variational Discretizations of Gauge Field Theories using Group-equivariant Interpolation
Foundations of Computational Mathematics, 19(5), 965-989, 2019.
Interpolation on Symmetric Spaces via the Generalized Polar Decomposition
(with E.S. Gawlik), Foundations of Computational Mathematics, 18(3), 757-788, 2018.
Lie Group Spectral Variational Integrators
(with J. Hall), Foundations of Computational Mathematics, 17(1), 199-257, 2017.
Spectral Variational Integrators
(with J. Hall), Numerische Mathematik, 130 (4), 681-740, 2015.
Generating Functionals and Lagrangian PDEs
(with C. Liao, J. Vankerschaver), Journal of Mathematical Physics, 54(8), 082901 (22 pages), 2013.
The Hamilton-Pontryagin Principle and Multi-Dirac Structures for Classical Field Theories
(with J. Vankerschaver, H. Yoshimura), Journal of Mathematical Physics, 53(7), 072903 (25 pages), 2012.
Variational and Geometric Structures of Discrete Dirac Mechanics
(with T. Ohsawa), Foundations of Computational Mathematics, 11(5), 529-562, 2011.
Discrete Hamilton-Jacobi Theory
(with A.M. Bloch, T. Ohsawa), SIAM Journal on Control and Optimization, 49(4), 1829-1856, 2011.
Geometric Tracking Control of a Quadrotor UAV on SE(3)
(with T. Lee, N.H. McClamroch), Proc. IEEE Conf. on Decision and Control, 5420-5425, 2010.
Lagrangian Mechanics and Variational Integrators on Two-Spheres
(with T. Lee, and N.H. McClamroch), International Journal for Numerical Methods in Engineering, 79(9), 1147-1174, 2009.
Lie Group Variational Integrators for the Full Body Problem
(with T. Lee, and N.H. McClamroch), Comput. Methods Appl. Mech. Engrg. 196(29-30), 2907-2924, 2007.
