Analytical Methods in Dynamics and Vibrations

3 Credits

This course will mainly cover the following topics: coordinate systems, conservations laws, inertial frames, systems of particles, DAE sets, variable-mass systems, transport equation, review of some of the basic concepts from variational calculus, D’Alembert’s principle, Hamilton’s principle, Lagrange multipliers, generalized momenta, 3D rigid-body motion, Inertia matrices, Euler angles, inertial and elastic coupling, discrete eigenvalue problem, linearization of nonlinear systems, chaotic systems, Hamilton’s principle for continuous systems, Torsion, Sturm-Liouville equations, Rayleigh’s quotient, finite-element eigen-problems, interpolating functions, combined-effect vibrations, and some other related topics.