Abstract The formulation for the dynamic analysis of undamped linear structural systems using the finite element method results in two element matrices; the mass and stiffness matrices, that describe the element inertia and stiffness properties. However, these matrices are not sufficient to describe the dynamics of structures that undergo large rigid-body motion. Other element matrices, in addition to the mass and stiffness matrices, are required to account for the inertia coupling between gross motion and elastic deformation. These matrices are time-invariant and can be generated and assembled in the same manner as the mass and stiffness matrices are assembled in linear structural dynamics. An inherent relation between these matrices and the deformable body mean axes exists. This paper is the first of two parts. It presents the two-dimensional and three-dimensional formulation of the system equations of motion of inertia-variant flexible bodies. In particular, Euler parameters are employed to describe the rotations of the body reference in the spatial analysis. In Part II [13], this formulation is applied to the impact analysis of a large-scale constrained flexible aircraft which are modeled as a multi-body system consisting of interconnected rigid and flexible components.
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