# American Institute of Mathematical Sciences

December  2013, 5(4): 381-397. doi: 10.3934/jgm.2013.5.381

## Discrete second order constrained Lagrangian systems: First results

 1 Depto. de Matemática, Facultad de Ciencias Exactas, UNLP, Instituto Balseiro, UNCu - CNEA - CONICET, 50 y 115, La Plata, Buenos Aires, 1900, Argentina 2 Instituto Balseiro, Universidad Nacional de Cuyo – C.N.E.A., Av. Bustillo 9500, San Carlos de Bariloche, R8402AGP 3 Instituto Balseiro, UNCu - CNEA - CONICET, Av. Bustillo 9500, San Carlos de Bariloche, R8402AGP, Argentina

Received  March 2013 Revised  November 2013 Published  December 2013

We briefly review the notion of second order constrained (continuous) system (SOCS) and then propose a discrete time counterpart of it, which we naturally call discrete second order constrained system (DSOCS). To illustrate and test numerically our model, we construct certain integrators that simulate the evolution of two mechanical systems: a particle moving in the plane with prescribed signed curvature, and the inertia wheel pendulum with a Lyapunov constraint. In addition, we prove a local existence and uniqueness result for trajectories of DSOCSs. As a first comparison of the underlying geometric structures, we study the symplectic behavior of both SOCSs and DSOCSs.
Citation: Nicolás Borda, Javier Fernández, Sergio Grillo. Discrete second order constrained Lagrangian systems: First results. Journal of Geometric Mechanics, 2013, 5 (4) : 381-397. doi: 10.3934/jgm.2013.5.381
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