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Exploiting Evolutionary Computation Techniques for Service Industries
Published in R.S. Chauhan, Kavita Taneja, Rajiv Khanduja, Vishal Kamra, Rahul Rattan, Evolutionary Computation with Intelligent Systems, 2022
Alejandro Rodríguez-Molina, José Solís-Romero, Miguel Ángel Paredes-Rueda, Carlos Alberto Guerrero-León, Manuel Eduardo Mora-Soto, Axel Herroz Herrera
For the EMLF-IC, the system model is derived from Lagrangian mechanics, a reformulation of classical mechanics that simplifies the analysis of mechanisms by considering the system energies (Gignoux & Silvestre-Brac, 2009). Therefore, the model corresponds to the Euler-Lagrange equations of motion in (8.2), where t is the time, L is the system Lagrangian, D is the Rayleigh dissipation function, qi is the i-th generalized coordinate, Qi is the i-th generalized force/torque, and n is the number of generalized coordinates. In this equation, the Lagrangian L=K−U is the difference between the total kinetic energy K and the total potential energy U of the system. At the same time, the Rayleigh dissipation function D involves the non-conservative effects in the system. Additional details on Lagrangian mechanics can be consulted in (Ogata, 2004).
Three-dimensional soliton-like distortions in flexoelectric nematic liquid crystals: modelling and linear analysis
Published in Liquid Crystals, 2022
Ashley Earls, M. Carme Calderer
Here denotes the Lagrangian of the system, that is, the difference of the density of kinetic energy ), the density of potential energy , and represents the elastic force [28]. The variational statement of this equation is where is the total energy of the system and . That is, the system behaves in such a way that the rate of work is minimised with respect to the generalised velocities. Letting represent the Rayleigh dissipation function, the dissipative forces are given by . The dynamics of a dissipative system is then formulated as the balance of the conservative forces by the dissipative ones, that is, the statement
A variational derivation of the thermodynamics of a moist atmosphere with rain process and its pseudoincompressible approximation
Published in Geophysical & Astrophysical Fluid Dynamics, 2019
A classical approach to include dissipation phenomena in Euler-Lagrange dynamics is due to Rayleigh (1877). This approach applies when the work done by dissipative actions can be expressed in terms of a Rayleigh dissipation function depending on the configuration q and velocity of the mechanical system. In abstract mechanical notations, the associated variational formulation takes the form and yields the Euler-Lagrange equations with dissipative force where it is assumed . We refer, for instance, to dell'Isola et al. (2009) for an application of (8) as a modelling tool in continuum mechanics.