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Journal of Applied Nonlinear Dynamics 13(3) (2024) 449--459 | DOI:10.5890/JAND.2024.09.003

Vijay K. Shukla$^{1}$, Anupam Priyadarshi$^{2}$, Shivam Shukla$^{1}$, Prashant K. Mishra$^{3}$

$^{1}$ Department of Mathematics, Shiv Harsh Kisan P.G. College, Basti-272001, India

$^{2}$ Department of Mathematics, Faculty of Science, Banaras Hindu University, Varanasi-221005, India

$^{3}$ Department of Mathematics, P. C. Vigyan Mahavidyalaya, Jai Prakash University, Chapra-841301, India

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Abstract

In this article, the mechanical analysis of Vallis system has been studied. Firstly, the Vallis system has been transformed into Kolmogorov type system, which is decomposed into four types of torques: inertial torque, internal torque, dissipation and external torque. Five scenarios are examined using combinations of various torques in order to identify the key elements in chaos creation and their physical significance. In these five scenarios, the conversion between kinetic energy, potential energy, and Hamiltonian energy is examined. It is examined how the energy and the parameters are interacting. The study comes to the conclusion that any combination of three forms of torques cannot create chaos in a Vallis system, and that a combination of these four types of torques is required to do so.

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