Week 1: Rigid body and coordinate systems, position and orientation, rotation matrices and their properties, Euler angles, quaternions, homogeneous transformation matrices and their properties, examples
Week 2: Linear and angular velocity of a rigid body, skew symmetric angular velocity matrix, space fixed and body fixed angular velocity, linear and angular acceleration, Coriolis/centripetal acceleration, velocities and accelerations in terms of Euler angles/quaternions, examples
Week 3: Joints in multi-body systems, joint variables, Degree-of-freedom and constraints due to a joint and in multi-body systems, holonomic and non-holonomic constraints, velocity and acceleration of rigid bodies in a multi-body system, alternate system of coordinates and resulting constraints, examples
Week 4: Mass and inertia of a rigid body, Properties of inertia matrix, external forces and moments acting on a rigid body -- gravity, friction, actuator torque/forces, angular momentum – example of spinning top and gyroscope.
Week 5: Free-body diagram, Newton-Euler formulation and equations of motion, Introduction to recursive formulations, examples.
Week 6: Equations of motion using Lagrangian formulation – rolling of a thin disk in 3D, two link robot and 4-bar mechanism, solution of equations of motion in Matlab, comparison between Newton-Euler and Lagrangian formulation.
Week 7: Modeling and simulation of multi-body systems using computer tools, examples using Simscape.
Week 8: Linearization of equations of motion, state space formulation, state variables, solution of state equations
Week 9: Stability, controllability and observability in SISO systems, examples
Week 10: Root locus and Bode plots, relationships between classical and state space approaches
Week 11: Design of controllers using state space and root locus.
Week 12: Case studies in modeling and control – planar robot, pendulum on a cart, stabilization using gyroscope etc.