Question

(25%) Let $\mathcal{F}_t: B \rightarrow \mathbb{R}_t \subset \mathbb{E}_3$, $t \in [t_0, t_1]$ be a motion of a body. For some $t_* \in [t_0, t_1]$, choose $\mathcal{F} = \mathcal{F}_{t_}$ as the reference configuration. Let $R = R_{t_}$. By using the results of previous problem, show that $\mathcal{L}(x, t_) = \mathbf{F}(x, t_)$ $\mathcal{D}(x, t_) = \mathbf{U}(x, t_)$ $\mathcal{W}(x, t_) = \mathbf{R}(x, t_)$

          (25%) Let $\mathcal{F}_t: B \rightarrow \mathbb{R}_t \subset \mathbb{E}_3$, $t \in [t_0, t_1]$ be a motion of a body. For some $t_* \in [t_0, t_1]$, choose $\mathcal{F} = \mathcal{F}_{t_*}$ as the reference configuration. Let $R = R_{t_*}$. By using the results of previous problem, show that
$\mathcal{L}(x, t_*) = \mathbf{F}(x, t_*)$ 
$\mathcal{D}(x, t_*) = \mathbf{U}(x, t_*)$ 
$\mathcal{W}(x, t_*) = \mathbf{R}(x, t_*)$

$(25%) Let $\mathcal{F}t: B \rightarrow \mathbb{R}t \subset \mathbb{E}3$, $t \in [t0, t1]$ be a motion of a body. For some $t* \in [t0, t1]$, choose $\mathcal{F} = \mathcal{F}{t*}$ as the reference configuration. Let $R = R{t*}$. By using the results of previous problem, show that ℒ(x, t*) = 𝐅(x, t*) 𝒟(x, t*) = 𝐔(x, t*) 𝒲(x, t*) = 𝐑(x, t*)$

Added by Nathaniel G.

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