Energy-preserving, Adaptive Time-Step Lie Group Variational Integrators for the Attitude Dynamics of a Rigid Body

Sharma, Harsh; Lee, Taeyoung

doi:10.23919/acc.2019.8815131

Cited by 2 publications

(1 citation statement)

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“…The same integrators were derived through a variational approach for a more general case of timedependent Lagrangian systems in [3] by preserving the discrete energy obtained from the discrete variational principle in the extended phase space. Recently, Sharma et al extended these methods to systems with external nonconservative forcing [6] and rigid body motion [7,8].…”

Section: Introductionmentioning

confidence: 99%

Performance Assessment of Energy-preserving, Adaptive Time-step Variational Integrators

Sharma,

Borggaard,

Patil

et al. 2021

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A fixed time-step variational integrator cannot preserve momentum, energy, and symplectic form simultaneously for nonintegrable systems. This barrier can be overcome by treating time as a discrete dynamic variable and deriving adaptive time-step variational integrators that conserve the energy in addition to being symplectic and momentum-preserving. Their utility, however, is still an open question due to the numerical difficulties associated with solving the governing discrete equations. In this work, we investigate the numerical performance of energy-preserving, adaptive time-step variational integrators. First, we compare the time adaptation and energy performance of the energy-preserving adaptive algorithm with the adaptive variational integrator for Kepler's problem. We also study the effect of variable precision arithmetic on the energy conservation properties. Second, we apply tools from Lagrangian backward error analysis to investigate numerical stability of the energy-preserving adaptive algorithm. Finally, we consider a simple mechanical system example to illustrate our backward stability approach by constructing a modified Lagrangian for the modified equation of an energy-preserving, adaptive time-step variational integrator.

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