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.
Copyright © 2013 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Gangopadhyaya, Asim, and Gordon Ramsey. “Unintended Consequences of Imprecise Notation: An Example from Mechanics.” American Journal of Physics 81, no. 4 (April 1, 2013): 313–15. doi:10.1119/1.4769255 and may be found at http://dx.doi.org/10.1119/1.4769255.