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

• 作者: Haiduke Sarafian
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: Velocity-Dependent Resistive Media Envelope of Trajectories Computational Mathematics and Physics Mathematica
• 年，卷（期）: 2020,（3）
• 页码范围: 431-440
• 页数: 10页
• 分类号: O17

摘要

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. <em>Mathematica</em> [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.