Lie derivative plays a key role in mathematics and physics. In particular, the Lie derivative discretization scheme has been implemented for a relatively large time step in order to quickly solve the numerical solution of the system. In this paper, an algorithm of the Lie derivative discretization scheme is applied to variable mass systems. Four different types of variable mass systems are employed to study the numerical solutions, and the calculated results are consistent with those obtained by the fourth-order Runge-Kutta method. Computational experiments demonstrate the success of the proposed method on variable mass systems. Moreover, the algorithm of Lie derivative discretization is shown to have superior computational efficiency and larger time steps compared to the Runge-Kutta algorithm.
Cao Z, Kang H, Liu H. Modeling and dynamic response of variable mass system of maglev turning electric spindle. *Nonlinear Dynamics*. 2023;111(1):255–74.
2.
Chen W, Chen G, Chen T. Dynamic response analysis of a typical time-varying mass system: A moving-interface pipe model, the WKB-recursive solution and experimental validation. *Applied Mathematical Modelling*. 2024;125:147–66.
3.
Cveticanin L. Dynamic buckling of a single-degree-of-freedom system with variable mass. *European Journal of Mechanics A/Solids*. 2001;20(4):661–72.
4.
Cveticanin L. A review on dynamics of mass variable systems. *Journal of the Serbian Society for Computational Mechanics*. 2012;6:56–73.
5.
Cveticanin L. *Dynamics of Bodies with Time-Variable Mass*. 2016.
6.
Flores J, Solovey G, Gil S. Variable mass oscillator. *American Journal of Physics*. 2003;71(7):721–5.
7.
Gouin H. Remarks on the Lie derivative in fluid mechanics. *International Journal of Non-Linear Mechanics*. 2023;150:104347.
8.
Hurtado JE. Analytical dynamics of variable-mass systems. *Journal of Guidance, Control, and Dynamics*. 2018;41(3):701–9.
9.
Irschik H, Holl HJ. Mechanics of variable-mass systems—Part 1: Balance of mass and linear momentum. *Applied Mechanics Reviews*. 2004;57(2):145–60.
10.
Iavernaro F, Mazzia F, Mukhametzhanov MS, Sergeyev YD. Computation of higher order Lie derivatives on the Infinity Computer. *Journal of Computational and Applied Mathematics*. 2021;383:113135.
11.
Letellier C, Mendes EM, Mickens RE. Nonstandard discretization schemes applied to the conservative Hénon-Heiles system. *International Journal of Bifurcation and Chaos*. 2007;17(3):891–902.
12.
Meena GD, Janardhanan S. Taylor-Lie formulation based discretization of nonlinear systems. *International Journal of Dynamical Control*. 2018;6:459–67.
13.
Mendes EM, Billings SA. A note on discretization of nonlinear differential equations. *Chaos*. 2002;12(1):66–71.
14.
Mendes E, Letellier C. Displacement in the parameter space versus spurious solution of discretization with large time step. *Journal of Physics A: Mathematical and General*. 2004;37(4):1203–18.
15.
Monaco S, Normand-Cyrot D. A combinatorial approach of the nonlinear sampling problem. In: *9th International Conference on Analysis and Optimization of Systems*, Lecture Notes in Control and Information Sciences. 1990. p. 20, 788–97.
16.
Nhleko S. Free vibration states of an oscillator with a linear time-varying mass. *Journal of Vibration and Acoustics*. 2009;145(6):051011.
17.
Zhang X, Li H. Exploiting multiple-frequency bursting of a shape memory oscillator. *Chaos, Solitons & Fractals*. 2022;158:112000.
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