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How do I reconcile these two definitions of acceleration?
How do I reconcile these two definitions of acceleration?
$$a=\frac{d\bar{v}}{dt}=(\frac{dv^k}{dt}+v^i v^j \Gamma^k_{ij})\bar{e}_k \tag{1}$$
and
$$a^k=v^{\small\beta} \nabla_{\small\beta} v^k.\tag{2}$$...
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