Dx

dqidqi qi

3qi V

dxj dq2

dqi dqi

we conclude from Eq. (A. 13) that d / 3 Xi dt \dqi dx, dqi

The following relations can be proven in a similar manner:

dt \dqi

Now let us use Eqs. (A. 11), (A. 12), (A. 15), and (A. 16) to calculate the function d fdK\ 3K dt \3<?i ) dqi '

for which the result is d (dK\ 3K

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