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Generalized Lagrangian dynamics of physical and non-physical systems

Author

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  • Sandler, U.

Abstract

In this paper, we show how to study the evolution of a complex system, given imprecise knowledge about the state of the system and the dynamics laws. It will be shown that dynamics of these systems is equivalent to Lagrangian (or Hamiltonian) mechanics in a n+1-dimensional space, where n is a system’s dimensionality. In some cases, however, the corresponding Lagrangian is more general than the usual one and could depend on the action. In this case, Lagrange’s equations gain a non-zero right side proportional to the derivative of the Lagrangian with respect to the action. Examples of such systems are unstable systems, systems with dissipation and systems which can remember their history. Moreover, in certain situations, the Lagrangian could be a set-valued function. The corresponding equations of motion then become differential inclusions instead of differential equations. We will also show that the principal of least action is a consequence of the causality principle and the local topology of the state space and not an independent axiom of classical mechanics.

Suggested Citation

  • Sandler, U., 2014. "Generalized Lagrangian dynamics of physical and non-physical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 1-20.
    • Handle: RePEc:eee:phsmap:v:416:y:2014:i:c:p:1-20
    DOI: 10.1016/j.physa.2014.08.016
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    Cited by:

    1. Sandler, U. & Tsitolovsky, L., 2017. "The S-Lagrangian and a theory of homeostasis in living systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 540-553.
    2. Sandler, U., 2017. "S-Lagrangian dynamics of many-body systems and behavior of social groups: Dominance and hierarchy formation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 218-241.
    3. Sandler, U., 2023. "Evolutionary quantization and matter-antimatter distribution in accelerated expanding of Universe," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 611(C).

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