Sarafian, Haiduke (2020) Global Characteristics of the Envelope of Family of Trajectories in Resistive Media. American Journal of Computational Mathematics, 10 (03). pp. 431-440. ISSN 2161-1203
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Abstract
In our recent article [1], we discussed the universal geometric characteristics of the envelope of family of trajectories of projectiles projected with the same speeds and different velocities in a vertical plane under the sole influence of gravity; our current investigation is its natural extension. As shown in [1] even for the simplest case where gravity is the only acting external agent literature overlooked reveling the characteristics of the envelope such as its arc-length, the surface area of the enclosed surface and etc. Calculation leading to these has carried out mostly longhand [1]. The current extended version embodies a realistic scenario where the projectiles in addition to gravity encounter linear velocity-dependent media resistance. In order to fulfil objectives similar to [1], we develop two distinct strategies obtaining the analytic equation for the envelope. On one hand, we solve the equations of motion applying traditional longhand approach. On the other hand, we adopt a Computer Algebra System (CAS), e.g. Mathematica [2] [3]. Having these outputs at hand, via mixed-mode calculation—some longhand and some via CAS—we explore its global geometric characteristics such as its arc-length, the surface area of the enclosure. Because of the calculation complexities we could not have achieved our set goals.
Item Type: | Article |
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Subjects: | AP Academic Press > Mathematical Science |
Depositing User: | Unnamed user with email support@apacademicpress.com |
Date Deposited: | 28 Jun 2023 04:36 |
Last Modified: | 18 Jun 2024 07:03 |
URI: | http://info.openarchivespress.com/id/eprint/1554 |