大変形挙動を伴う柔軟梁のダイナミクスと変分的積分法

抄録

It is well known that a flexible space structure such as a beam antenna attached to spacecraft performs large deformations due to the overall motion of its base, and it is crucial to make a model that includes the effect of geometrical nonlinearity between displacements, rotations and strains. The geometrically exact model has been known as a powerful tool to analyze dynamics of such a flexible space structure. In this paper, we show the variational principle of Hamilton for the infinite dimensional dynamical system to apply to a flexible beam attached to its base undergoing large overall motions. Then, we develop a structure-preserving variational integrator which is known to be superior in long-term computations for energy. In particular, we examine two types of space discretization methods; namely, the trapezoidal rule that yields explicit difference equations and the midpoint rule that yields implicit equations. Finally we make comparisons of these two types of space discretization methods in the variational integrators.