Applied Dynamics is an important branch of engineering mechanics widely applied to mechanical and automotive engineering, aerospace and biomechanics as well as control engineering and mechatronics. The computational methods presented are based on common fundamentals. For this purpose analytical mechanics turns out to be very useful where D'Alembert's principle in the Lagrangian formulation proves to be most efficient. The method of multibody systems, finite element systems and continuous systems are treated consistently. Thus, students get a much better understanding of dynamical phenomena, and engineers in design and development departments using computer codes may check the results more easily by choosing models of different complexity for vibration and stress analysis.
Werner Schiehlen is Professor Emeritus of Mechanics and Past Head of the Institute of Engineering and Computational Mechanics of the University of Stuttgart, Stuttgart, Germany. He has published widely on topics such as multibody system dynamics, nonlinear dynamics, random vibrations, optimization, contact problems, biomechanics, mechatronics, robotics, and vehicle dynamics. He has won many awards and honours and served his field in many capacities in Germany and in the rest of the world. He is one of the Editors in Chief of the Springer journal Multibody System Dynamics. Peter Eberhard is also a Professor at the Institute of Engineering and Computational Mechanics of the University of Stuttgart, originally studying under Professor Schiehlen. Professor Eberhard also has (co-)authored many works, has international experience, and serves as board member for acclaimed journals. Together they developed the course material presented here, continually improving and adapting it to new insights and current requirements, first in German, now published in English for a global readership.
Introduction.- Purpose of applied dynamics.- Contribution of analytical mechanics.- Modeling of mechanical systems.- Multibody systems.- Finite-Element systems.- Continuous systems.- Flexible multibody systems.- Choice of a mechanical model.- Degrees of freedom.- Basics of kinematics.- Free systems.- Kinematics of a point.- Kinematics of the rigid body.- Kinematics of the continuum.- Holonomic systems.- Point systems.- Multibody systems.- Continuum.- Nonholonomic systems.- Relative motion of the coordinate frame.- Moving coordinate system.- Free and holonomic systems.- Nonholonomic systems.- Linearization of the kinematics.- Basics of dynamics.- Dynamics of a point.- Newtons equations.- Types of forces.- Dynamics of the rigid body.- Newtons and Eulers equations.- Mass geometry of the rigid body.- Relative motion of coordinate systems.- Dynamics of the continuum.- Cauchys equations.- Hookes material law.- Reaction stresses.- Principles of mechanics.- Principle of virtual work.- Principle of d'Alembert, Jourdain and Gauss.- Principle of minimal potential energy.- Hamiltons principle.- Lagrange equations of first kind.- Lagrange equations of second kind.- Multibody systems.- Local equations of motion.- Newton-Euler equations.- Equations of motion of ideal systems.- Simple mutlibody systems.- General multibody systems.- Reaction forces of ideal systems.- Computation of reaction forces.- Strength estimation.- Balancing of masses in multibody systems.- Equations of motion and reaction equations of non ideal systems.- Gyroscopic equations of satellites.- Formalisms for multibody systems.- Non recursive formalisms.- Recursive formalisms.- Finite-Elemente systems.- Local equations of motion.- Tetrahedral elements.- Spatial beam element.- Global equations of motion.- Beam systems.- Strength computations.- Continuous systems.- Local equations of motion.- Eigen functions of bars.- Global equations of motion.- State equations of mechanical systems.- Nonlinear state equations.- Linear state equations.- Transformation of linear equations.- Normal forms.- Numerical equations.- Integration of nonlinear differential equations.- Linear algebra for time variant systems.- Comparison of mechanical models.- Appendix.- A Mathematical tools.- Representation of functions.- Matrix algebra.- Matrix analysis.- List of important variables.- Bibliography.- Index.