A geometrical interpretation and uniform matrix formulation of multibody system dynamics

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Lie-group integration method for constrained multibody systems in state space (2014, background): “As it is well-known from the classical MBS literature [4, 22, 23] and research papers in the field (see, for example, [24] and references cited there or [25]), the integration results of (13) should also satisfy kinematical constraints on the position and velocity level (10c) and (11) (so-called ‘hi”
Review of Classical Approaches for Constraint Enforcement in Multibody Systems (2008, background): “Blajer [41, 42] summarized much of the work done within the framework of differential Riemannian geometry: index1 formulation, NSF, and Maggi’s formulation for combined holonomic and nonholonomic constraints have all been presented in this framework.”
A Geometric Approach to Solving Problems of Control Constraints: Theory and a DAE Framework (2004, background): “The dynamic equations (1) of the controlled system at hand can be projected into two complementary subspaces of the n-space E, the defined above m-dimensional constrained (orthogonal) subspace C, and the l-dimensional (l = n − m) unconstrained (tangent) subspace D, C ∪ D = N and C ∩ D = 0. The compl”