Construction and analysis of higher order variational integrators for dynamical systems with holonomic constraints

DOI10.1007/s10444-017-9520-5zbMath1378.65186OpenAlexW2592246484MaRDI QIDQ1683229

Sina Ober-Blöbaum, Sigrid Leyendecker, Theresa Wenger

Publication date: 6 December 2017

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://ora.ox.ac.uk/objects/uuid:9346ca38-6731-4663-99d8-0603e4d5ec1d

zbMATH Keywords

numerical exampleEuler-Lagrange equationsLagrange multiplierholonomic constraintsdifferential algebraic equationorder reductionnumerical convergence analysisvariational integratorstime reversibilityhigher-order integrationsymplectic momentum methods

Mathematics Subject Classification ID

Numerical methods for differential-algebraic equations (65L80) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items

Symplectic P-stable additive Runge-Kutta methods ⋮ Construction and analysis of higher order variational integrators for dynamical systems with holonomic constraints ⋮ Constructing time integration with controllable errors for constrained mechanical systems ⋮ Preservation of adiabatic invariants for disturbed Hamiltonian systems under variational discretization ⋮ The GGL variational principle for constrained mechanical systems ⋮ High order symmetric algorithms for nonlinear dynamical systems with non-holonomic constraints ⋮ Galerkin Lie-group variational integrators based on unit quaternion interpolation ⋮ Higher order finite elements in space and time for anisotropic simulations with variational integrators. Application of an efficient GPU implementation ⋮ Multisymplectic Galerkin Lie group variational integrators for geometrically exact beam dynamics based on unit dual quaternion interpolation -- no shear locking ⋮ Linear-Time Variational Integrators in Maximal Coordinates ⋮ Variational integrators for forced Lagrangian systems based on the local path fitting technique ⋮ A discrete mechanics approach for musculoskeletal simulations with muscle wrapping

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Construction and analysis of higher order Galerkin variational integrators
• Geometric generalisations of SHAKE and RATTLE
• An introduction to Lie group integrators - basics, new developments and applications
• Symplectic numerical integrators in constrained Hamiltonian systems
• Collocation methods for differential-algebraic equations of index 3
• Global modified Hamiltonian for constrained symplectic integrators
• Construction and analysis of higher order variational integrators for dynamical systems with holonomic constraints
• The numerical solution of differential-algebraic systems by Runge-Kutta methods
• Convergence of Runge-Kutta methods for differential-algebraic systems of index 3
• Spectral variational integrators
• Variational and linearly implicit integrators, with applications
• A Variational Approach to Multirate Integration for Constrained Systems
• Discrete mechanics and optimal control for constrained systems
• Discrete mechanics and variational integrators
• Specialized Partitioned Additive Runge–Kutta Methods for Systems of Overdetermined DAEs with Holonomic Constraints
• Structure Preservation for Constrained Dynamics with Super Partitioned Additive Runge--Kutta Methods
• Galerkin variational integrators and modified symplectic Runge–Kutta methods
• Symplectic Partitioned Runge–Kutta Methods for Constrained Hamiltonian Systems
• Symplectic Integration of Constrained Hamiltonian Systems by Composition Methods
• Geometric Numerical Integration
• Variational integrators for constrained dynamical systems