This graduate level course on Analytical Dynamics is based on an integrated approach that combines the classical methodology of dynamical systems modelling (following Lagrange, Hamilton and Jacobi) with the analytical and geometrical developments of nonlinear mechanics (proposed by Lyapunov and Poincare'). This approach enables a comprehensive and rigorous treatment of both multiple rigid-body and continuous dynamical systems incorporating: i) formulation of constrained (non-holonomic) spatio-temporal models (via the variational Hamilton's principle), ii) solution derivation of nonlinear models via exact (integrals of motion, separatrices) and approximate singular perturbation (averaging, asymptotic multiple-scales) methods culminating with slowly varying evolution equations, iii) qualitative behavior of solutions (integrability, symmetry, periodicity, orbital stability, synchronization). Examples include applications to interdisciplinary problems governing the domain of dynamical systems that can only be described by several types of generalized coordinates/forces, such as robotics/mechatronics, nano/micro-electromechanical systems, and thermo-visco-elastic dynamics and fluid-structure interaction. The objectives of this course are to introduce, develop and apply the fundamentals of analytical dynamics required for derivation, solution and analyses of nonlinear problems that govern engineering mechanics.
- Teacher: עודד גוטליב