Validation of new rigid body dynamics formulation using rotation matrices elements as dependent parameters - double pendulum case study


  • Dan D. Dumitriu
  • Mihai Margaritescu


rigid body dynamics, rotation matrix elements, orthogonality condition, Lagrange multipliers, algebro-differential system, double pendulum


The method of using the rotation matrix elements as dependent parameters for the 3D rotation of a rigid body is currently very rarely used in multibody dynamics. Nevertheless, this redundant parameterization of 3D rotations presents advantages, as well as disadvantages, with respect to classical independent parameters or less dependent parameters (e.g., quaternions). Thus, when using rotation matrix elements as dependent parameters, the dynamics of a rigid multibody system consists of solving an algebrodifferential equations system comprising 12 scalar differential equations plus 6 algebraic scalar orthogonality equations per solid, plus the algebraic equations characterizing the articulations between the linked solids of the multibody system. The disadvantage of such an increased number of parameters/equations for our method is fully compensated by the fact that the dynamics equations can be written in a systematic way, being structurally similar for each solid. This paper validates our new rigid body dynamics formulation on the double pendulum case study, proposing a simplified version of the Lagrange multipliers elimination method. More precisely, a two-step elimination method is proposed to solve the algebraic part of the algebro-differential equations system.


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