Lagrange’s Equations for Rocket-Type Variable Mass Systems

Nanjangud, Angadh; Eke, Fidelis O.

doi:10.15866/irease.v5i5.15613

Cited by 5 publications

(8 citation statements)

References 9 publications

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“…where H * 0 is the angular momentum of the variable mass system and is (12) Since V = V 0 at a particular instant, H * and H * 0 are identical but their time derivatives are generally not identical since their evolution in time is associated with changing sets of matter. Since our interest is in understanding the behavior of the variable mass system's angular momentum from an inertial frame, we revert the time derivative in Equation (11)…”

Section: Angular Momentum Of a Variable Mass Systemmentioning

confidence: 99%

“…A control volume approach [8,9] to account for continuous mass variation subsequently emerged which has since become the modeling standard amongst the community of researchers on rocket flight dynamics. Recent work using the control volume formulation has focused on equation of motion formulation for general variable mass systems [10,11], modeling and analysis of rocket-type systems [12][13][14][15] and an abstraction of the rocket problem [16], and stability of transverse rotational motion in solid rocket motors [17]. The developments presented here on angular momentum also utilize this control volume formulation.…”

Section: Introductionmentioning

confidence: 99%

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Angular momentum of free variable mass systems is partially conserved

Nanjangud

Eke

2018

Aerospace Science and Technology

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Variable mass systems are a classic example of open systems in classical mechanics with rockets being a standard practical example. Due to the changing mass, the angular momentum of these systems is not generally conserved. Here, we show that the angular momentum vector of a free variable mass system is fixed in inertial space and, thus, is a partially conserved quantity. It is well known that such conservation rules allow simpler approaches to solving the equations of motion. This is demonstrated by using a graphical technique to obtain an analytic solution for the second Euler angle that characterizes nutation in spinning bodies.

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Section: Angular Momentum Of a Variable Mass Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Angular momentum of free variable mass systems is partially conserved

Nanjangud

Eke

2018

Aerospace Science and Technology

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“…Understanding the dynamics of systems with variable mass is of great relevance, for instance, to the study of ship and rocket motions [7][8][9][10]. In the present paper we characterize the CM of a particle system in two different scenarios: a) when the number of particles in the system varies by one unit, and this transition happens in a very short time, but all particle masses are constant; b) when the number of particles in the system is fixed, but the mass of one of them varies in time.…”

Section: Introductionmentioning

confidence: 99%

Center of mass of a system of variable mass particles

Thomaz

Silva

2019

Rev. Bras. Ensino Fís.

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We study the dynamics of the center of mass (CM) of a set of particles when the number of particles in the system varies during a short interval of time, or when the value of the mass of one of the particles depends on time. We show that in both situations, while the population or mass of the system varies, the linear momentum of the CM differs from the total linear momentum of the system. During this time interval, the dynamics of the CM is driven by the external forces that act on the system plus transient forces that depend on the position and velocity of the CM. This dynamics is applied to study the time evolution of the vector position of the CM of a system of free particles moving on an air rail in which the mass of one the particles varies in a short time interval. We want to show it to students that with the knowledge and tools they have at an elementary Mechanics course they can formulate and answer questions which are not in the textbooks.

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“…and appropriately invoking Reynold's Transport Theorem. This approach has been discussed in several papers [5][6][7]. The following is the equation of attitude motion of a general variable mass system…”

Section: Introductionmentioning

confidence: 99%

“…ρ exit is the assumed density of exhaust gases on the exit plane. Substituting Equations (6), (7), (8), and (9) into Equation (2) yieldṡ…”

Section: Introductionmentioning

confidence: 99%

Geometry of motion and nutation stability of free axisymmetric variable mass systems

Nanjangud

2018

Nonlinear Dyn

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In classical mechanics, the 'geometry of motion' refers to a development to visualize the motion of freely spinning bodies. In this paper, such an approach of studying the rotational motion of axisymmetric variable mass systems is developed. An analytic solution to the second Euler angle characterising nutation naturally falls out of this method, without explicitly solving the nonlinear differential equations of motion. This is used to examine the coning motion of a free axisymmetric cylinder subject to three idealized models of mass loss and new insight into their rotational stability is presented. It is seen that the angular speeds for some configurations of these cylinders grow without bounds. In spite of this phenomenon, all configurations explored here are seen to exhibit nutational stability, a desirable property in solid rocket motors.allows Equations (11) and (12) to be combined to yield a differential equation linear in ω c :

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Lagrange’s Equations for Rocket-Type Variable Mass Systems

Cited by 5 publications

References 9 publications

Angular momentum of free variable mass systems is partially conserved

Angular momentum of free variable mass systems is partially conserved

Center of mass of a system of variable mass particles

Geometry of motion and nutation stability of free axisymmetric variable mass systems

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