Laurent Jay
Institute
University of Iowa
Address
Department of Mathematics
14 MacLean Hall
Iowa City, IA 52242-1419
USA
Presentation
oral
(Plenary talk)
Title
Lagrange-d'Alembert integrators for constrained systems in mechanics
Abstract
Numerical methods in discrete mechanics attempt to reproduce
continuous concepts from mechanics at a discrete level. For
example variational integrators for unconstrained Lagrangian systems satisfy
a discrete Hamilton's variational principle, symplectic
methods for Hamiltonian systems satisfy a discrete symplectic
condition. In this talk we will consider Lagrangian
systems with holonomic and nonholonomic constraints.
Such systems can be expressed as overdetermined systems of
differential-algebraic equations (DAEs) and they can be
derived from the Lagrange-d'Alembert principle which is
one of the most fundamental principles in classical mechanics.
We define a new discrete Lagrange-d'Alembert principle for Lagrangian
systems with constraints based on a discrete Lagrange-d'Alembert principle
for forced Lagrangian systems. Constraints are considered as first
integrals of the underlying forced Lagrangian system of
ordinary differential equations. A large class of specialized
partitioned additive Runge-Kutta (SPARK) methods satisfies the
new discrete principle. We will show that symmetric Lagrange-d'Alembert
SPARK integrators of any order can be obtained based for example on
Gauss and Lobatto coefficients. We will also discuss how SPARK
methods can be implemented efficiently.
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