Variational integrators for mechanical control systems with symmetries
DOI10.3934/jcd.2015003zbMath1397.70024arXiv1209.6315OpenAlexW2398679337MaRDI QIDQ317181
David Martín de Diego, Fernando Jiménez, Leonardo Colombo
Publication date: 30 September 2016
Published in: Journal of Computational Dynamics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1209.6315
optimal controlvariational integratorsconstrained mechanicsdiscrete variational calculushigher-order mechanicsunderactuated systems
Geometric methods in ordinary differential equations (34A26) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) Existence theories for free problems in one independent variable (49J05) Hamiltonian and Lagrangian mechanics (70Hxx)
Related Items (6)
Cites Work
- High order variational integrators in the optimal control of mechanical systems
- On the dynamic Markov-Dubins problem: from path planning in robotics and biolocomotion to computational anatomy
- Geometric dynamics of optimization
- Higher order Lagrange-Poincaré and Hamilton-Poincaré reductions
- Variational reduction of Lagrangian systems with general constraints
- Symplectic groupoids and discrete constrained Lagrangian mechanics
- Optimal attitude control of a rigid body using geometrically exact computations on \(SO(3)\)
- Geometric structure-preserving optimal control of a rigid body
- Invariant higher-order variational problems
- Geometric control and numerical aspects of nonholonomic systems
- Nonholonomic Lagrangian systems on Lie algebroids
- Hamilton-Pontryagin integrators on Lie groups. I: Introduction and structure-preserving properties
- Symmetry reduction of discrete Lagrangian mechanics on Lie groups
- Nonholonomic mechanics and control. With the collaboration of J. Baillieul, P. Crouch, and J. Marsden. With scientific input from P. S. Krishnaprasad, R. M. Murray, and D. Zenkov.
- On variational integrators for optimal control of mechanical control systems
- Mechanical integrators derived from a discrete variational principle
- Discrete variational optimal control
- Discrete second order constrained Lagrangian systems: first results
- A geometric approach to discrete connections on principal bundles
- Higher-order variational problems on Lie groups and optimal control applications
- Variational principles for constrained systems: Theory and experiment
- Lagrangian reduction by stages
- Hamiltonian dynamics and constrained variational calculus: continuous and discrete settings
- Discrete mechanics and optimal control: An analysis
- Discrete mechanics and optimal control for constrained systems
- Discrete mechanics and variational integrators
- High Order Variational Integrators: A Polynomial Approach
- DISCRETE SECOND-ORDER EULER–POINCARÉ EQUATIONS: APPLICATIONS TO OPTIMAL CONTROL
- Optimal control of underactuated mechanical systems: A geometric approach
- Inexact trajectory planning and inverse problems in the Hamilton–Pontryagin framework
- Higher-order discrete variational problems with constraints
- HIGHER-ORDER DISCRETE LAGRANGIAN MECHANICS
- Discrete Lagrangian and Hamiltonian mechanics on Lie groupoids
- Discrete calculus of variations
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Variational integrators for mechanical control systems with symmetries
