  Sensitivity analysis for multibody systems formulated on a Lie groupSonneville, Valentin  ; Bruls, Olivier in Multibody System Dynamics (2013) A direct differentiation method and an adjoint variable method are proposed for the efficient semi-analytical evaluation of the sensitivities of multibody systems formulated in a matrix Lie group ... [more ▼] A direct differentiation method and an adjoint variable method are proposed for the efficient semi-analytical evaluation of the sensitivities of multibody systems formulated in a matrix Lie group framework. These methods rely on the linearization of the equations of motion and/or of the time integration procedure. The simpler structure of the equations of motion in the Lie group formalism appears as an advantage for that purpose. Lie bracket contributions and the non-linearity of the exponential map need to be taken into account in the sensitivity algorithms. Nevertheless, essential characteristics of formulations of the direct differentiation method and the adjoint variable method on linear spaces are recovered. Some implementation issues are discussed and two relevant examples illustrate the properties of these methods. [less ▲] Detailed reference viewed: 19 (2 ULg)Formulation of Kinematic Joints and Rigidity Constraints in Multibody Dynamics using a Lie Group ApproachSonneville, Valentin ; Bruls, Olivier in Proceedings of the 2nd Joint International Conference on Multibody System Dynamics (IMSD) (2012, May) The matrix Lie group approach allows to formulate and solve the equations of motion of a multibody system in a parametrization-free framework. The kinematic joints and the rigidity constraints should also ... [more ▼] The matrix Lie group approach allows to formulate and solve the equations of motion of a multibody system in a parametrization-free framework. The kinematic joints and the rigidity constraints should also be formulated as constraint equations on the Lie group. Working on the Special Euclidean group SE(3), we introduce a method to obtain appropriate vectorial constraint equations in terms of mixed coordinates. Moreover, we present an absolute coordinates formulation, based on an relative coordinates elimination method, so that the minimum number of constraint equations necessary to describe the joints is used. [less ▲] Detailed reference viewed: 24 (6 ULg) Sensitivity analysis for flexible multibody systems formulated on a Lie groupBruls, Olivier ; Sonneville, Valentin Conference (2012, February) Detailed reference viewed: 17 (5 ULg) |
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