engleski

Angular Momentum Conserving Integration Scheme for Multibody System Dynamics in Lie-Group Setting

In many engineering applications, such as satellite dynamics or various case-studies of the specific locomotion patterns in mechatronics and biomechanics, motion integrals of the system need to be conserved during numerical integration in order to reflect global physical properties of the analysed motion. Derivation of such integration schemes in Lie-group settings should be especially efficient since Lie-group dynamical models operate directly on SO(3) rotational matrices and angular velocities, avoiding local rotation parameters and artificial algebraic constraints as well as kinematical differential equations (differential equations that relate body rotation parameters’ derivatives and angular velocity). In this paper, different mathematical models and angular momentum conserving integration schemes, based on Lie-group DAE index 1 formulation of the system dynamics, will be investigated and tested through the several case-studies, such as satellite dynamics with the internal kinematical chain.

Lie-groups; Numerical Integration Methods; DAE systems; Angular Momentum Conservation; Constraint Violation Stabilization

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