ENGR 5240G - Advanced Dynamics

This course builds upon the knowledge students have gained in a first dynamics course to cover more advanced dynamical systems. Topics covered will include 3D kinematics and kinetics of particles and systems of particles using Newton’s method; equations of motion in normal and tangential, cylindrical and spherical coordinates; two body central force motion with applications in orbital dynamics and particle on a rotating earth. 3D kinematics and kinetics of rigid bodies, Euler angles, single and multiple rotating reference frames, Coriolis acceleration, inertial reference frames, equations of translational motion, angular momentum, rotational motion, body axes and rotation relative to a coordinate system, Euler’s and modified Euler’s equations of motion with applications in dynamics of gyroscopes, robots and vehicles. Variational mechanics, constraints, generalized coordinates, principles of virtual work, D’Alembert, and Hamilton’s principle, concept of Hamiltonian, Hamilton’s canonical equations. Lagrange’s equation for system of particles and rigid bodies, generalized force and moment, calculus of variations, concepts of Lagrangian and Lagrange multiplier, Lagrange’s equations for holonomic and nonholonomic systems, stability analysis of autonomous and non-autonomous dynamical systems. Numerical solutions of dynamic systems, explicit methods include finite difference and Rung-Kutta, and implicit methods are Houbolt, Wilsontheta, Park stuffy stable and Newark-beta.
Credit hours: 3