High Order Variational Integrators: A Polynomial Approach

DOI10.1007/978-3-319-06953-1_24zbMath1326.65173arXiv1307.6139OpenAlexW2127938851MaRDI QIDQ3448892

Cédric M. Campos

Publication date: 27 October 2015

Published in: Advances in Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.6139

zbMATH Keywords

optimal control problemsvariational integratorssymplectic Galerkin schemessymplectic Runge-Kutta schemes

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Existence theories for optimal control problems involving ordinary differential equations (49J15) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (4)

Variational order for forced Lagrangian systems ⋮ Variational integrators for mechanical control systems with symmetries ⋮ Retraction maps: a seed of geometric integrators ⋮ High order variational integrators in the optimal control of mechanical systems

Cites Work

• Integrable discrete-time systems and difference operators
• Discrete nonholonomic Lagrangian systems on Lie groupoids
• Geometric discretization of nonholonomic systems with symmetries
• Runge-Kutta methods in optimal control and the transformed adjoint system
• Discrete Lagrange-d'Alembert-Poincaré equations for Euler's disk
• Discrete mechanics and optimal control: An analysis
• Geometric Numerical Integration
• Discrete mechanics and variational integrators
• DISCRETE SECOND-ORDER EULER–POINCARÉ EQUATIONS: APPLICATIONS TO OPTIMAL CONTROL
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