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Energy considerations for the stabilization of constrained mechanical systems with velocity projection

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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 behavior affects the stability of the numerical scheme, resulting in the use of stabilization techniques based on enforcing the invariants. A coordinate projection is a post-stabilization 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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  1. ETSI Caminos, Canales y Puertos, Universidad Politécnica de Madrid, C/Profesor Aranguren s/n, 28040, Madrid, Spain

    Juan C. García Orden

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  1. Juan C. García Orden
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Correspondence to Juan C. García Orden.

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García Orden, J.C. Energy considerations for the stabilization of constrained mechanical systems with velocity projection. Nonlinear Dyn 60, 49–62 (2010). https://doi.org/10.1007/s11071-009-9579-8

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  • DOI: https://doi.org/10.1007/s11071-009-9579-8

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