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\ddot{\mathbf{r}}_{A}=\mathbf{L}\ddot{\mathbf{q}}+\dot{\mathbf{L}}\dot{\mathbf{q}}={\left[\begin{array}{l}{0.66}\\ {22.32}\end{array}\right]}+{\left[\begin{array}{l}{-46.702}\\ {-4.159}\end{array}\right]}={\left[\begin{array}{l}{-46.042}\\ {18.161}\end{array}\right]}\,\mathrm{m}/\mathrm{sec}^{2}
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$$
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<<<<<<< HEAD
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# 5.2 INERTIA OF DEFORMABLE BODIES
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=======
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# 5.2 INERTIA OF DEFORMABLE BODIES 可變形體的慣性
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>>>>>>> gitea/master
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In this section, we develop the kinetic energy of deformable bodies and point out the differences between the inertia properties of deformable bodies that undergo finite rotations and the inertia properties of both rigid and structural systems. In addition to the inertia tensor and the conventional mass matrix that appear, respectively, in rigid body dynamics and the dynamics of linear structural systems, **it will be shown that a set of inertia shape integrals that depend on the assumed displacement field must be evaluated in order to completely define the mass matrix of deformable bodies that undergo large reference rotations.** Moreover, the body inertia tensor depends on the elastic deformation and, as a consequence, is time-variant.
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在本节中,我们将推导可变形体的动能,并指出在有限转动下,可变形体的惯性特性与刚体和结构体系的惯性特性之间的差异。除了分别出现在刚体动力学和线性结构体系动力学中的惯性张量和传统质量矩阵之外,我们将展示需要**计算一组取决于假设位移场的惯性形状积分**,才能完全定义在发生大参考转动的可变形体的质量矩阵。 此外,体惯性张量取决于弹性变形,因此是随时间变化的。
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