wizard85
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Homework Statement
If {\vec{V}(t) is a vector function of t, find the indefinite integral:
\int (\vec{V}\times \frac{d^2\vec{V}}{dt^2}) \,dt
Homework Equations
The Attempt at a Solution
I have solved it by decomposing and integrating each terms of vector \vec{V}\times \frac{d^2t}{dt^2}, so I have:
<br /> \vec{V}\times \frac{d^2\vec{V}}{dt^2}= \hat i (V_y * \frac{d^2V_z}{dt^2} - V_z * \frac{d^2V_y}{dt^2}) - \hat j (V_x * \frac{d^2V_z}{dt^2} - V_z * \frac{d^2V_x}{dt^2}) + \hat k (V_x * \frac{d^2V_y}{dt^2} - V_y * \frac{d^2V_x}{dt^2})<br />
and the integral will be:
<br /> <br /> \int (\vec{V}\times \frac{d^2\vec{V}}{dt^2}) \,dt = \hat i (\int (V_y * \frac{d^2V_z}{dt^2})\,dt - \int (V_z * \frac{d^2V_y}{dt^2})\,dt) - \hat j (\int (V_x * \frac{d^2V_z}{dt^2})\,dt - \int (V_z * \frac{d^2V_x}{dt^2}))\,dt + \hat k (\int (V_x * \frac{d^2V_y}{dt^2})\,dt - \int (V_y * \frac{d^2V_x}{dt^2}),dt)<br /> <br />where \hat i,\hat j and \hat k are the three unit vectors with respect to frame of reference (x,y,z)My questions is: that's the right way or there exist some other way to resolve it in a more faster manner?
Thanks to all who will answer me ;)
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