A Brief Review on Equation of Motion of Variable Mass System
DOI:
https://doi.org/10.47134/physics.v2i3.1723Keywords:
Newton's second law, Galilean invariance, Variable mass systemAbstract
Newton’s second law states that the external force acting on a system is equal to the rate of change of its linear momentum. It is Galilean invariant when the system mass is constant. There is a misunderstanding that Newton’s second law is neither a valid expression nor Galilean invariant in case of variable mass system. In a variable mass system, total system mass is a still remaining constant but remnant and ejected masses vary with time at equal rates. In case of rocket, system total mass always constant but remnant mass decreasing with time and ejected mass is increasing with time at equal rates. In the existing literature equation of motion of variable system considered as equation of motion of present remnant mass. In this work we consider total mass, remnant mass and ejected mass are three different systems and Newton's law validity and its Galilean invariance are verified for these three systems.
References
Alameh, A. (2024). Rocket Motion. arXiv preprint arXiv:2406.00055.
DeMarini, D. M. (2022). Mutagenicity and carcinogenicity of combustion emissions are impacted more by combustor technology than by fuel composition: A brief review. Environmental and Molecular Mutagenesis, 63(3), 135-150, ISSN 0893-6692, https://doi.org/10.1002/em.22475
Elliott, A.J. (2025). In-orbit system identification of a flexible satellite with variable mass using dual Unscented Kalman filters. Acta Astronautica, 226, 71-86, ISSN 0094-5765, https://doi.org/10.1016/j.actaastro.2024.11.014
Gavrilov, S.N. (2024). Formal asymptotics for oscillation of a discrete mass-spring-damper system of time-varying properties, embedded into a one-dimensional medium described by the telegraph equation with variable coefficients. Nonlinear Dynamics, 112(23), 20967-21002, ISSN 0924-090X, https://doi.org/10.1007/s11071-024-10154-4
Goldstein, H. (2011). Classical Mechanics. India: Pearson Education.
Halliday, D., Resnick, R., & Walker, J. (2011). Fundamentals of physics (9 ed.). New York: John Wiley & Sons, Inc.,.
Jarzębowska, E. (2024). Modeling Of Constrained Variable Mass Systems Based Upon The Boltzmann-Hamel Approach. Proceedings of the ASME Design Engineering Technical Conference, 9, https://doi.org/10.1115/DETC2024-143040
Jiang, Z. (2024). A fast primal-dual algorithm via dynamical system with variable mass for linearly constrained convex optimization. Optimization Letters, 18(8), 1855-1880, ISSN 1862-4472, https://doi.org/10.1007/s11590-023-02091-9
Kaczmarczyk, G. (2025). Deep-Learning Techniques Applied for State-Variables Estimation of Two-Mass System. Energies, 18(3), ISSN 1996-1073, https://doi.org/10.3390/en18030568
Kalinin, Y. (2024). Solving Problems of Dynamics of Systems with Elastic Elements and Variable Masses. Lecture Notes in Networks and Systems, 1129, 179-192, ISSN 2367-3370, https://doi.org/10.1007/978-3-031-70670-7_15
Kostka, Z. (2024). Dynamics Modeling Of Variable Mass Systems – A Case Study Of An Underwater Inertia Based Propelled Glider Performance. Journal of Theoretical and Applied Mechanics, 62(4), 751-761, ISSN 1429-2955, https://doi.org/10.15632/jtam-pl/194505
Lam, K. F. (2024). Stability and convergence of relaxed scalar auxiliary variable schemes for Cahn-Hilliard systems with bounded mass source. Journal of Numerical Mathematics, 32(3), 233-255, ISSN 1570-2820, https://doi.org/10.1515/jnma-2023-0021
Morin, D. (2008). Introduction to classical mechanics: with problems and solutions. Cambridge University Press.
Peraire, J. &. (2008). Lecture L14-Variable Mass Systems: The Rocket Equation. Dynamics.
Pesce, C. (2020). Mechanics of variable mass systems - a historic perspective.
Punthupeng, S. (2024). Development Of A Structural Equation Model Of The Variables Affecting The Organizational Performance Of The Mass Rapid Transit Systems Of Thailand. Revista De Gestao Social E Ambiental, 18(2), ISSN 1981-982X, https://doi.org/10.24857/RGSA.V18N2-083
Suhir, E. (2022). Predictive modeling sheds useful light on burn-in testing (BIT): Brief review and recent extension. Microelectronics Reliability, 128, ISSN 0026-2714, https://doi.org/10.1016/j.microrel.2021.114371
Simmonds, J. (2020). The role of agent-based modeling and multi-agent systems in flood-based hydrological problems: A brief review. Journal of Water and Climate Change, 11(4), 1580-1602, ISSN 2040-2244, https://doi.org/10.2166/wcc.2019.108
Wang, B. (2024). Heuristic deepening of aero engine performance analysis model based on thermodynamic principle of variable mass system. Energy, 306, ISSN 0360-5442, https://doi.org/10.1016/j.energy.2024.132481
Zhang, H. W. (2025). Dynamic Response Analysis of the Turning Variable Mass Hydrostatic Spindle System. International Journal of Precision Engineering and Manufacturing, ISSN 2234-7593, Https://Doi.Org/10.1007/S12541-025-01219-4
Zhang, Y. (2025). A mathematical and numerical model for variable cross-section hull girder with time-varying mass systems applied in marine vessels. Marine Structures, 101, ISSN 0951-8339, https://doi.org/10.1016/j.marstruc.2024.103726
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Veera Reddy Vippala
This work is licensed under a Creative Commons Attribution 4.0 International License.
