Originally Posted by **Pmb** In the first place you omitted the dot product sign. Put that in and get the expression for T which is T = Sum over all i { (1/2)m_i x v_i^2}
where v_i^2 = **v**_i dot **v**_i
Then take the derivative with respect to q_i (which has a dot over it which I don't know how to do)
If this is unclear I'll do it out on paper scan it then post it. |

ok, fixed the latex above. Copied it from the textbook wrong (and didn't have access to codecogs equation editor and my hand typed latex not too great). Didn't realise they were vectors. (

Caiken M.G. textbook, pg 42) was a bit unclear on this when they developed the equations. Looked like they were expressing the formulas purely in terms of the vector components.

Read your attached page. I saw your product rule expansion of the kinetic energy formula. Seems you haven't gone as far as showing how the dot's cancel yet? I presume there is more to this than just the product rule.

I did eventually find this video on the internet:

Seems to rely on equating two different expressions for r_dot. I can see the result but it seems not to be geometrically intuitive.