• Mukesh Kumar
• Abhi Raj

In classical mechanics, various approaches have been formulated based on the concepts of force, energy, least action path, etc. They could be applied to figure out the motion equations for conservative systems, making them effective tools for system predictions. It is also possible to extend it to non-conservative environments. In this work, we have extended the physical system with dissipating factor prediction, with the help of the "Euler-Lagrange equation, Hamilton’s principle, and the least action principle". Such an explanation argues that an object will always select the path that requires the least amount of action, irrespective of any dissipating factor. But as we move to higher dissipating factors the optimal nature of action is lost. All these make systems nonlinear with an integer dissipating factor which indirectly depends on the system and surrounding nature. A brief analysis of system dynamics was studied up to the third order of dissipation, especially for spring-mass system. It is found that dissipating variables affect not only velocity variables but also perturbed path/action integrals. The Hamiltonian is conserved in the case of non-forced oscillation. The more sensitive behavior of damping environments on a time scale is also noted.

"A study of dissipative Systems based on LAP", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.10, Issue 12, page no.e566-e573, December-2023, Available :http://www.jetir.org/papers/JETIR2312469.pdf

"A study of dissipative Systems based on LAP", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.10, Issue 12, page no. ppe566-e573, December-2023, Available at : http://www.jetir.org/papers/JETIR2312469.pdf