Martin Bjerre Nielsen

Rigid Body Time Integration by Convected Base Vectors with Implicit Constraints

A conservative time integration algorithm based on a convec ted set of orthonormal base vectors is presented. The equations of motion are deriv ed from an extended Hamiltonian formulation, combining the components of the three base vec tors with a set of orthonormality constraints. The particular form of the kinetic energy used in the present formulation is deliberately chosen to correspond to a rigid body rotation, and th e orthonormality constraints are introduced via the equivalent Green strain components of th e base vectors. The particular form of the extended inertia tensor used here implies a set of orth ogonality relations between the base vector components and their conjugate momentum components . The e orthogonality relations permit explicit elimination of the Lagrange multipliers as sociated with the constraints, leading to a projected form of the dynamic equation without explicit algebraic constraints. The differential equations of motion are recast into discrete form usi ng a suitable combination of mean values and increments, which is identified by considering a fi nite increment of the Hamiltonian. Examples illustrate the accuracy and conservation propert ies of the algorithm. S. Krenk and M.B. Nielsen