Rigid Body Time Integration By Convected Base Vectors With Implicit Constraints

Abstract eng:
A conservative time integration algorithm based on a convected set of orthonormal base vectors is presented. The equations of motion are derived from an extended Hamiltonian formulation, combining the components of the three base vectors 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 the orthonormality constraints are introduced via the equivalent Green strain components of the base vectors. The particular form of the extended inertia tensor used here implies a set of orthogonality relations between the base vector components and their conjugate momentum components. These orthogonality relations permit explicit elimination of the Lagrange multipliers associated 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 using a suitable combination of mean values and increments, which is identified by considering a finite increment of the Hamiltonian. Examples illustrate the accuracy and conservation properties of the algorithm.

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