engleski

Differential-Geometric Concepts in Numerical ODE/DAE Integration of Mechanical Systems

The paper reviews issues of geometric modeling of dynamics of discrete mechanical systems with the special focus on mathematical models and numerical procedures for computational forward dynamics of multibody systems with holonomic and non-holonomic kinematical constraints. Starting with the configuration space of rigid body motion and analysis of it’s Lie group structure, the elements of respective Lie algebra are addressed and relations pertinent to geometric formulations and integration of multibody system dynamics are surveyed. Dynamical model of unconstrained multibody systems on manifolds are introduced, along with the outline of geometric characteristics of holonomic and non-holonomic kinematical constraints. Time integration numerical algorithms for constrained multibody systems in the form of ODE on manifolds, expressed in the local integration coordinates, as well as DAE systems via redundant coordinates, are reviewed. Numerical stabilization algorithms for kinematical constraints violation are addressed. The generalized coordinates partitioning algorithm is analysed in the context of the issue of optimal partitioning of system coordinates within the framework of local ODE integration as well as projective stabilization algorithms for holonomic and non-holonomic multibody systems.

discrete mechanical systems; geometric integration; holonomic and non-holonomic; constraints; Lie groups; ODE on manifolds; constraint violation stabilization; multibody systems

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