Physics Commons^™

Unintended Consequences Of Imprecise Notation – An Example From Mechanics, Asim Gangopadhyaya, Gordon Ramsey

Asim Gangopadhyaya

We present a conundrum that results from the imprecise use of notation for partial derivatives. Taking an example from mechanics, we show that lack of proper care in re presenting partial derivatives in Lagrangian and Hamiltonian formulations paradoxically leads to two different values for the time derivative of the canonical momentum. This problem also exists in other areas of physics,such as thermodynamics.