Multibody Dynamics

Introduction: Rigid-body mechanics, Multibody systems, Reference frames and frame transformations, Derivatives of vector functions, Eigen-value analysis, Classification of multibody mechanical systems – Serial and Closed-loops.

Reference Kinematics: Rotation matrix, Successive rotations, Moving coordinate frames, Properties of Rotation Matrix, Velocity and Accelerations and important identities, Rodrigues parameters, Euler angles, Direction Cosines, Homogeneous Transformations, Orientation Coordinates.

Lagrangian Dynamics: Mass/Inertia distribution, Generalized coordinates and kinematic constraints, Degrees-of-freedom, Virtual work and Generalized forces and energy functions, Lagrangian dynamics, Application to rigid body dynamics.

Analytical Techniques: Calculus of Variations, Euler’s equation for several variables, Formulation of equations of motion. Application to two and three degrees-of-freedom mechanisms, Newton-Euler Equations, Applications to multibody linearization and integrals of equations of motion, Extraction of information from equations of motion

Mechanics of deformable bodies: Kinematics of deformable bodies, Stress components and strain components, Equation of equilibrium, Constitutive equations and Elastic forces.

Numerical lab: Numerical Algorithms for Inverse and Forward dynamics, Computational issues, Efficiency and numerical stability aspects of algorithms, multibody dynamics simulations in software platform like Simscape(MATLAB).

Attendance is mandatory in the course.

The evaluation is going to consist of 2 tests (10 each), mid-term(20), programming/analysis assignments(30) , final exam(30).

The programming assignments can be done on MATLAB/Python.

Other than extreme grades (A and F), the grading is going to be relative.