A review on extension of Lagrangian-Hamiltonian mechanics

Rastogi, Vipul; Mukherjee, A.; Dasgupta, Anirban

doi:10.1590/s1678-58782011000100004

Cited by 4 publications

(2 citation statements)

References 39 publications

(58 reference statements)

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“…[9] and briefly presented in Appendix for ready reference of the readers. Some basic concepts of umbra-Lagrangian density have been provided in reference [6,7,11].…”

Section: Formulation Of Extended Noether's Theoremmentioning

confidence: 99%

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Effects of Discrete Damping on the Dynamic Behaviour of Rotating Shaft through Extended Lagrangian Formulation

Rastogi¹

2016

Journal of Theoretical and Applied Mechanics

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Abstract. The main focus of the paper is touted as effects of discrete damping on the dynamic analysis of rotating shaft. The whole analysis is being carried out through extended Lagrangian formulation for a discrete -continuous system. The variation formulation for this system is possible, considering the continuous system as one-dimensional. The generalized formulation for one dimensional continuous rotary shaft with discrete external damper has been obtained through principle of variation. Using this extended formulation, the invariance of umbra-Lagrangian density through extended Noether's theorem is achieved. Rayleigh beam model is used to model the shaft. Amplitude equation of rotor is obtained theoretically and validated through simulation results. The simulation results reveal the important phenomena of limiting dynamics of the rotor shaft, which is due to an imbalance of material damping and stiffness of the rotor shaft. The regenerative energy in the rotor shaft, induced due to elasticity/stiffness of the rotor shaft, is dissipated partially through the inspan discrete damper and also through the dissipative coupling between drive and the rotor shaft. In such cases, the shaft speed will not increase with increase in excitation frequency of the rotor but the slip between the drive and the shaft increases due to loading of drive.

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“…[9] and briefly presented in Appendix for ready reference of the readers. Some basic concepts of umbra-Lagrangian density have been provided in reference [6,7,11].…”

Section: Formulation Of Extended Noether's Theoremmentioning

confidence: 99%

“…The bond graph model [11,28,29] of the continuous shaft with in span concentrated external damping is simulated in SYMBOLS-Sonata [30,31] software, in order to visualize the complex modes of the system. However, the external damping in sub models of shaft has been considered as discrete or finite.…”

Section: Simulation Studiesmentioning

confidence: 99%