2014
DOI: 10.1007/978-3-319-06953-1_24
|View full text |Cite
|
Sign up to set email alerts
|

High Order Variational Integrators: A Polynomial Approach

Abstract: We reconsider the variational derivation of symplectic partitioned Runge-Kutta schemes. Such type of variational integrators are of great importance since they integrate mechanical systems with high order accuracy while preserving the structural properties of these systems, like the symplectic form, the evolution of the momentum maps or the energy behaviour. Also they are easily applicable to optimal control problems based on mechanical systems as proposed in Ober-Blöbaum et al. [2011].Following the same appro… Show more

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1
1

Citation Types

0
8
0

Year Published

2015
2015
2024
2024

Publication Types

Select...
4
1

Relationship

0
5

Authors

Journals

citations
Cited by 6 publications
(8 citation statements)
references
References 9 publications
0
8
0
Order By: Relevance
“…Thus, it generates a new symplectic integrator. Moreover, it is possible to compose more than two Lagrangian submanifolds to generate more involved methods where the intermediate points γ q play the role of micro-nodes (see [11,35,41]).…”
Section: Discrete Variational Calculusmentioning
confidence: 99%
“…Thus, it generates a new symplectic integrator. Moreover, it is possible to compose more than two Lagrangian submanifolds to generate more involved methods where the intermediate points γ q play the role of micro-nodes (see [11,35,41]).…”
Section: Discrete Variational Calculusmentioning
confidence: 99%
“…With some abuse of notation we denote the force and the cost functions defined on T * Q × U and T * Q, respectively, by F (q, p, u) := F (q, f (q, p), u), C(q, p, u) := C(q, f (q, p), u) and Φ(q, p) := Φ(q, f (q, p)) such that Problem 2.1 can be formulated as an optimal control problem for the partitioned system (6). subject toq…”
Section: 2mentioning
confidence: 99%
“…Besides notice that the first two equations define p 1/2 and q 1 implicitly and that the whole set reduces to the Verlet method for a constant λ. Indeed, it is shown in [6,38] that for a Lagrangian with constant mass matrix and Lobatto quadrature rule, the sG and the spRK method coincide.…”
Section: High Order Variational Integrators High Order Variational In...mentioning
confidence: 99%
See 1 more Smart Citation
“…Lett. 110 174301) and Galley et al (2014( arXiv:1412). We show that this construction is useful to design high-order integrators for forced Lagrangian systems and, more importantly, we give a characterization of the order of a method applied to a forced system using the corresponding variational order of the duplicated one.…”
mentioning
confidence: 98%