4 citations · 5 across the 7 of their papers we have counts for
7 papers
A Geometric Approach to Structure-Preserving Integrators for Mechanical Systems
Viyom Vivek, David Martin de Diego, Ravi N. Banavar
We develop a geometric framework for the numerical integration of mechanical systems evolving on manifolds. After briefly reviewing classical numerical methods and highlighting the…
Jacobi equation for field theories and a geometric variational description of dissipation
David Martin de Diego, Najma Mosadegh
In this paper we give a geometric description of the Jacobi equations associated to a first-order Lagrangian field theory using a prolongation of the Lagrangian on a -cosymp…
Numerical Integrators for Mechanical Systems on Lie Groups
Viyom Vivek, David Martin de Diego, Ravi N Banavar
Retraction maps are known to be the seed for all numerical integrators. These retraction maps-based integrators can be further lifted to tangent and cotangent bundles, giving rise…
Retraction maps: A seed of geometric integrators. Part II: Symmetry and reduction
María Barbero Liñán, Juan Carlos Marrero, David Martín de Diego
In this paper we use retraction and discretization maps (see [Barbero Liñán and Martín de Diego, 2022]) as a tool for deriving in a systematic way numerical integrators preserving…
Reduction by symmetries of contact mechanical systems on Lie groups
Alexandre Anahory Simoes, Leonardo Colombo, Manuel de León +3
We study the dynamics of contact mechanical systems on Lie groups that are invariant under a Lie group action. Analogously to standard mechanical systems on Lie groups, existing sy…
Linear connections and shape maps for second order ODEs with and without constraints
G. E. Prince, M. Farré Puiggalí, D. J. Saunders +1
We deal with the construction of linear connections associated with second order ordinary differential equations with and without first order constraints. We use a novel method all…
Discrete dynamics in implicit form
D. Iglesias, J. C. Marrero, D. Martin de Diego +1
A notion of implicit difference equation on a Lie groupoid is introduced and an algorithm for extracting the integrable part (backward or/and forward) is formulated. As an applicat…