Global Characteristics of the Envelope of Family of Trajectories in Resistive Media

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

[thumbnail of ajcm_2020090815192565.pdf] Text
ajcm_2020090815192565.pdf - Published Version

Download (579kB)

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
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

Actions (login required)

View Item
View Item