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Apr 2013

Volume 81, Issue 4, pp. 245-319

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Unintended consequences of imprecise notation: An example from mechanics

Asim Gangopadhyaya and Gordon Ramsey

American Journal of Physics -- April 2013 -- Volume 81, Issue 4, pp. 313

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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.
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45.00.00 Classical mechanics of discrete systems
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