Given that \\(R=sin ¡t i+cos ¡t j+tk\\), find \\( (d^2 R)/(dt^2 )\\).
1
Expert's answer
2020-11-17T17:45:07-0500
First of all let us notice the fact that the basis vectors of R3(i,j,k) are constant (as opposed to local vectors er,eθ,ez of the cylindrical coordinates base, for example). Therefore the derivation of R(t) comes down to deriving every coordinate. Secondly, let us write R(t) as a vector for more obviousness:
R(t)=⎝⎛sin(a^t)cos(a^t)t⎠⎞
Now let's calculate the first and then the second derivative:
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