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The present book contains the 16 papers accepted and published in the Special Issue “Mathematical Modeling and Simulation in Mechanics and Dynamic Systems” of the MDPI “Mathematics” journal, which cover a wide range of topics connected to the theory and applications of Modeling and Simulation of Dynamic Systems in different field. These topics include, among others, methods to model and simulate mechanical system in real engineering. It is hopped that the book will find interest and be useful for those working in the area of Modeling and Simulation of the Dynamic Systems, as well as for those with the proper mathematical background and willing to become familiar with recent advances in Dynamic Systems, which has nowadays entered almost all sectors of human life and activity.

T-stress --- X-FEM --- notch --- pipe --- stress difference method (SDM) --- system of transcendental equation --- computational solutions --- code-based modelling approach --- numerical analysis --- Sine-Gordon equations --- photovoltaics --- thermophotovoltaics --- solar energy --- polymer CNTs systems --- interphase section --- percolation onset --- mechanics --- high temperature proton exchange membrane fuel cell --- exergy analysis --- ecological analysis --- ecological coefficient of performance --- SARS-CoV-2 --- COVID-19 --- SEIRD (Susceptible, Exposed, Infected and Recovered and Death) --- SDL --- Catalonia --- nanowire cantilever --- stochastic model --- double Lorentzian spectrum --- HT-PEMFC --- irreversibility --- finite time thermodynamic optimization --- power density --- thermodynamic efficiency --- geometric analogy --- similarity theory --- dimensional analysis --- model law --- heat transfer --- straight bar --- Deep Learning (DL) --- Computational Fluid Dynamics (CFD) --- Artificial Neural Network (ANN) --- Convolutional Neural Network (CNN) --- turbulent flow --- machine learning --- deep learning --- artificial neural network --- ANN --- PEM fuel cell --- modeling --- control --- differentiability --- fractal hydrodynamic regimes --- fractal Schrödinger regimes --- fractal soliton --- fractal kink --- “holographic implementations” --- cubics --- apolar transport --- harmonic mapping principle --- period doubling scenario --- state probability functions --- partial aging in standby --- Monte Carlo simulation --- qualitative and quantitative verification of simulation model --- Lagrange–d’Alembert principle --- non-conservative dynamical system --- Euler–Poincaré equation --- helicopter model --- Lie group --- extended iso-geometric analysis --- extended finite element method --- crack --- pipeline --- ABAQUS --- harmonic mapping --- complex system dynamics --- SL (2R) group --- hidden symmetries --- computer simulations --- actual systems --- transfer learning --- autonomous feature extraction --- n/a --- fractal Schrödinger regimes --- "holographic implementations" --- Lagrange-d'Alembert principle --- Euler-Poincaré equation