Linear Dynamics: Planar Kinetics and Kinematics of Rigid Bodies, 3D Rotation, Angular Velocity, Time Derivative of a Vector, Five-Term Acceleration Equation, Coriolis Acceleration, Phase Portrait, Virtual Work, D’A Lembert Principle, Lagrange Equations of Particles, Conservative Forces, Linearization, Free Vibration, Hamiltonian’s Principle, Lagrange Equations of Rigid Bodies, 15  Cyclic Variables, Hamiltonian, Lagrange Multiplier, Hamilton Canonical Equations, Ruth Equations, Moment of Inertia, Principals Directions, Euler Angles, Euler Equations. Nonlinear Dynamics: phase space, phase portraits, linear oscillators, equilibrium solutions (continuous systems and maps), stability concepts, linearization and stability analysis, bifurcation types, periodic solutions, Floquet theory, shooting technique, Poincare sections, quasi-periodic solutions, nonlinear oscillations, multiple scales, Duffing, secondary resonances, self-excitation, parametric excitation, chaos, crises escape from potential well, tangling.