Applied Dynamics

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.