Convergence Results for a Coordinate Projection Method Applied to Mechanical Systems with Algebraic Constraints

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  • EEEdda Eich
    Edda Eich
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Abstract
The equations of motion of mechanical multibody systems with algebraic constraints are of index 3 and therefore not directly solvable by standard ODE or DAE methods. Reducing the index by differentiating the constraints results in an ODE or reduced index DAE with invariants. The presence of discretization errors in the numerical solution leads to violations of the invariants and eventually yields a drift-off from the manifold given by the invariants. As a consequence one obtains physically meaningless solutions. To overcome this difficulty a coordinate projection method is presented, which projects the discretized solution onto the invariant manifold. Convergence theorems for a combination of the BDF-method and projection are given. The techniques used in the proof allow insight into the way the errors are propagated. In particular, it can be shown that only those parts of the errors lying in the manifold will be propagated. This leads to solutions which not only satisfy the invariant but are more accurate.

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