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math.OC2011
Quadratic choreographies
Philippe Ryckelynck, Laurent Smoch
This paper addresses the classical and discrete Euler-Lagrange equations for systems of particles interacting quadratically in . By highlighting the role played b…
math.OC2011
Discrete Calculus of Variations for Quadratic Lagrangians. Convergence Issues
Philippe Ryckelynck, Laurent Smoch
We study in this paper the continuous and discrete Euler-Lagrange equations arising from a quadratic lagrangian. Those equations may be thought as numerical schemes and may be solv…
math.OC2011
Discrete calculus of variations for quadratic lagrangians
Philippe Ryckelynck, Laurent Smoch
We develop in this paper a new framework for discrete calculus of variations when the actions have densities involving an arbitrary discretization operator. We deduce the discrete…