Unintended Consequences of Imprecise Notation – an Example from Mechanics

Asim Gangopadhyaya; Gordon Ramsey

doi:10.1119/1.4769255

Unintended Consequences of Imprecise Notation – an Example from Mechanics

Asim Gangopadhyaya, Gordon Ramsey

Department of Physics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	American English
Journal	Physics: Faculty Publications and Other Works
Volume	81
Issue number	4
DOIs	https://doi.org/10.1119/1.4769255
State	Published - Apr 1 2013

Keywords

Partial Differentiation
Classical Mechanics
Lagrangian Formulation
Hamiltonian Formulation

Disciplines

Physics

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abstract = " 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.",

keywords = "Partial Differentiation, Classical Mechanics, Lagrangian Formulation, Hamiltonian Formulation",

author = "Asim Gangopadhyaya and Gordon Ramsey",

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AB - 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.

KW - Partial Differentiation

KW - Classical Mechanics

KW - Lagrangian Formulation

KW - Hamiltonian Formulation

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Unintended Consequences of Imprecise Notation – an Example from Mechanics

Abstract

Keywords

Disciplines

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