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Fall with linear drag and Wien's displacement law: approximate solution and Lambert function

Abstract : We present an approximate solution for the downward time of travel in the case of a mass falling with a linear drag force. We show how a quasi-analytical solution implying the Lambert function can be found. We also show that solving the previous problem is equivalent to the search for Wien's displacement law. These results can be of interest for undergraduate students, as they show that some transcendental equations found in physics may be solved without purely numerical methods. Moreover, as will be seen in the case of Wien's displacement law, solutions based on series expansion can be very accurate even with few terms.
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https://hal-utt.archives-ouvertes.fr/hal-02329203
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Submitted on : Wednesday, October 23, 2019 - 2:42:19 PM
Last modification on : Friday, March 27, 2020 - 4:28:02 PM

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Alexandre Vial. Fall with linear drag and Wien's displacement law: approximate solution and Lambert function. European Journal of Physics, European Physical Society, 2012, 33 (4), pp.751-755. ⟨10.1088/0143-0807/33/4/751⟩. ⟨hal-02329203⟩

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