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Discretizing variational principles, as opposed to discretizing differential equations, leads to discrete-time analogues of mechanics, and, systematically, to geometric numerical integrators. The phase space of such variational discretizations is often the set of configuration pairs, analogously corresponding to initial and terminal points of a tangent… (More)

- George W. Patrick, Charles Cuell
- Numerische Mathematik
- 2009

Due to a singularity or degeneracy at zero time-step, existence and uniqueness, and accuracy, of variational integrators, cannot be established by straightforward use of the implicit function theorem. We show existence and uniqueness for variational integrators by blowing up the variational principle. The blow-up implies an accuracy one less than is… (More)

Skew critical problems occur in continuous and discrete nonholonomic Lagrangian systems. They are analogues of constrained optimization problems, where the objective is differentiated in directions given by an apriori distribution, instead of tangent directions to the constraint. We show semiglobal existence and uniqueness for nondegenerate skew critical… (More)

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