5 papers
On the functional equation
Philippe Ryckelynck, Laurent Smoch
We study in this paper the functional equation where , $\mathbf{u},\mathbf…
Discrete calculus of variation for homographic configurations in celestial mechanics
Philippe Ryckelynck, Laurent Smoch
We provide in this paper the discrete equations of motion for the newtonian -body problem deduced from the quantum calculus of variations (Q.C.V.) developed in \cite{Cre,CFT,RS1…
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…
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…
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…