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## Main Question or Discussion Point

I'm reading "The variational principles of mechanics", written by C. Lanczos and he said that, if one have the condition [itex]dq_3 = B_1 dq_1 + B_2 dq_2 [/itex] and one want to know if there is a finite relation between the [itex]q_i[/itex], on account the given condition, one must have the condition [tex] \frac{\partial B_1}{\partial q_2} = \frac{\partial B_2}{\partial q_1}[/tex].

What I don't understand is how the condition on the differentials imply the equality between the derivatives above.

What I don't understand is how the condition on the differentials imply the equality between the derivatives above.