Modelling the dynamics of bodies self-propelled by exponential mass exhaustion

Abstract

We present a study of the ascending vertical motion of a self-propelled body under a uniform gravitational field suffering the action of two different types of air friction forces: linear on the velocity, which is valid for slowly moving bodies, and quadratic on the velocity. We study the special case where the thrust force is a decreasing function of mass, which corresponds to the exponential mass exhaustion rate. We present in detail the analytical solutions for the equations of motion for the two types of air friction, and briefly present some techniques for solving the related ordinary differential equations. This paper is intended for undergraduate physics teachers and for graduate students.

Cohetes hidráulicos con videos en cámara lenta

“…La solución de esta ecuación queda determinada por la relación funcional que describe el drag (F drag ), el cambio de masaṁ en función de la densidad del fluido dentro del cohete debido a los cambios de presión. La solución a este problema ha sido ampliamente abordado en la literatura,empleando diferentes métodos de análisis [1][2][3][4]13,14,[21][22][23][24][25][26][27][28][29][37][38][39][40][41][42][43].…”

Dynamic population balance and flow models for granular solids in a linear vibrating screen

“…In classical mechanics, variable mass systems have historically been reserved for celestial mechanics, and the most practical it has gotten is in the physics laboratories and applied mathematics courses, e.g., the leaking oscillator experiments. Even though some physicists had started to take a keen interest on this aspect as early as 2008, they are yet to be applied on some key ground‐based industrial systems.…”

Analytical description of ascending motion of rockets in the atmosphere

“…Thus, we may define the exhaustion time, t E , as t E = m p /R. Inserting the last equation into equation (1) we obtain the differential equation…”

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In continuation of a previous work [1], we present an analytic study of ascending vertical motion of a rocket subjected to a quadratic drag for the case where the mass-variation law is a linear function of time. We discuss the detailed analytical solution of the model differential equations in closed form.

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“…In a previous work [1], we have analyzed the motion of self-propelled bodies in the atmosphere for the case of exponential mass exhaustion law. In this work, we present the case where the mass exhaustion follows a linear law.…”