Abstract
There are many difficulties involved in the numerical integration of index-3 Differential Algebraic Equations (DAEs), mainly related to stability, in the context of mechanical systems. An integrator that exactly enforces the constraint at position level may produce a discrete solution that departs from the velocity and/or acceleration constraint manifolds (invariants). This behaviour affects the stability of the numerical scheme, resulting in the use of stabilization techniques based on enforcing the invariants. A coordinate projection is a poststabilization technique where the solution obtained by a suitable DAE integrator is forced back to the invariant manifolds. This paper analyzes the energy balance of a velocity projection, providing an alternative interpretation of its effect on the stability and a practical criterion for the projection matrix selection.
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Notes
- 1.
Not necessarily the same employed for the velocity projection.
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Acknowledgements
The authors wish to acknowledge the financial support of the Spanish Ministry of Science and Innovation as part of project DPI-2006-15613-C03-02 under the name “Modelización numérica eficiente de grandes sistemas flexibles con aplicaciones de impacto”.
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Orden, J.C.G., Aguilera, R.A.O. (2011). Energy Considerations for the Stabilization of Constrained Mechanical Systems with Velocity Projection. In: Arczewski, K., Blajer, W., Fraczek, J., Wojtyra, M. (eds) Multibody Dynamics. Computational Methods in Applied Sciences, vol 23. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9971-6_8
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