TY - GEN
T1 - A lie group variational integrator for rigid body motion in SE(3) with applications to underwater vehicle dynamics
AU - Nordkvist, Nikolaj
AU - Sanyal, Amit K.
PY - 2010
Y1 - 2010
N2 - The topic of variational integrators for mechanical systems whose dynamics evolve on nonlinear spaces has seen strong growth recently. Within this class of variational integrators is the subclass of Lie group variational integrators that can be used for mechanical systems whose dynamics evolve on Lie groups. This class of mechanical systems includes all systems that can be modeled as rigid bodies or connections of rigid bodies. In this paper, we present a Lie group variational integrator for the full (translation and orientation) motion of a rigid body under the possible influence of nonconservative forces and torques. We use a discretization scheme for such systems which is based on the discrete Lagrange-d'Alembert principle to obtain the Lie group variational integrator. We apply the composition of the Lie group variational integrator with its adjoint and a Crouch-Grossman method to the example of a conservative underwater system. We show numerically that with respect to energy these manifold methods, as expected, behave as a symplectic integrator and a nonsymplectic integrator, respectively.
AB - The topic of variational integrators for mechanical systems whose dynamics evolve on nonlinear spaces has seen strong growth recently. Within this class of variational integrators is the subclass of Lie group variational integrators that can be used for mechanical systems whose dynamics evolve on Lie groups. This class of mechanical systems includes all systems that can be modeled as rigid bodies or connections of rigid bodies. In this paper, we present a Lie group variational integrator for the full (translation and orientation) motion of a rigid body under the possible influence of nonconservative forces and torques. We use a discretization scheme for such systems which is based on the discrete Lagrange-d'Alembert principle to obtain the Lie group variational integrator. We apply the composition of the Lie group variational integrator with its adjoint and a Crouch-Grossman method to the example of a conservative underwater system. We show numerically that with respect to energy these manifold methods, as expected, behave as a symplectic integrator and a nonsymplectic integrator, respectively.
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U2 - 10.1109/CDC.2010.5717622
DO - 10.1109/CDC.2010.5717622
M3 - Conference contribution
AN - SCOPUS:79951633608
SN - 9781424477456
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 5414
EP - 5419
BT - 2010 49th IEEE Conference on Decision and Control, CDC 2010
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 49th IEEE Conference on Decision and Control, CDC 2010
Y2 - 15 December 2010 through 17 December 2010
ER -