Variational Integrators for Dynamical Systems with Rotational Degrees of Freedom
نویسندگان
چکیده
For the elastodynamic simulation of a geometrically exact beam, a variational integrator is derived from a PDE viewpoint. Variational integrators are symplectic and conserve discrete momentum maps and since the presented integrator is derived in the Lie group setting (unit quaternions for the representation of rotational degrees of freedom), it intrinsically preserves the group structure without the need for constraints. The discrete Euler-Lagrange equations are derived in a general manner and then applied to the beam.
منابع مشابه
An Efficient Strain Based Cylindrical Shell Finite Element
The need for compatibility between degrees of freedom of various elements is a major problem encountered in practice during the modeling of complex structures; the problem is generally solved by an additional rotational degree of freedom [1-3]. This present paper investigates possible improvements to the performances of strain based cylindrical shell finite element [4] by introducing an additio...
متن کاملVariational Integrators for Maxwell’s Equations with Sources
In recent years, two important techniques for geometric numerical discretization have been developed. In computational electromagnetics, spatial discretization has been improved by the use of mixed finite elements and discrete differential forms. Simultaneously, the dynamical systems and mechanics communities have developed structure-preserving time integrators, notably variational integrators ...
متن کامل8 Variational Lie Group Formulation of Geometrically Exact Beam Dynamics: Synchronous and Asynchronous Integration
For the elastodynamic simulation of a geometrically exact beam [1], an asynchronous variational integrator (AVI) [2] is derived from a PDE viewpoint. Variational integrators are symplectic and conserve discrete momentum maps and since the presented integrator is derived in the Lie group setting (SO (3) for the representation of rotational degrees of freedom), it intrinsically preserves the grou...
متن کاملA Linear-Time Variational Integrator for Multibody Systems
We present an efficient variational integrator for simulating multibody systems. Variational integrators reformulate the equations of motion for multibody systems as discrete Euler-Lagrange (DEL) equation, transforming forward integration into a root-finding problem for the DEL equation. Variational integrators have been shown to be more robust and accurate in preserving fundamental properties ...
متن کاملConstructing Equivalence-preserving Dirac Variational Integrators with Forces
The dynamical motion of mechanical systems possesses underlying geometric structures, and preserving these structures in numerical integration improves the qualitative accuracy and reduces the long-time error of the simulation. For a single mechanical system, structure preservation can be achieved by adopting the variational integrator construction. This construction has been generalized to mor...
متن کامل