Unintended consequences of imprecise notation: An example from mechanics
Asim Gangopadhyaya, Gordon P. Ramsey · American Journal of Physics · 2013
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 representing partial derivatives in the Lagrangian and Hamiltonian formulations paradoxically leads to two different values for the time derivative of the canonical momentum. Similar apparent paradoxes occur in other areas of physics, such as thermodynamics.