This course provides a natural continuation of the course INGE 3032 (Engineering Mechanics: Dynamics). The main extension is advanced three-dimensional kinematics and dynamics, with illustrations of application to engineering problems. Additionally, this course is intended to serve as a bridge between a course on elementary dynamics of planar rigid bodies (e.g. INGE 3032) and a general-purpose computer-based course on flexible multibody dynamics (e.g. INME 5530). It is designed to equip students with fundamental theories and computational methodologies that are used in the analysis of rigid multibody systems. The emphasis is on an integrated understanding of: (i) modeling, (ii) modern vector/analytical rigid body dynamics equation formulation for complex systems, and (iii) computational solution techniques applied to mechanical multibody systems. Students will learn how to analytically formulate equations of motion for multibody systems as well as how to utilize numerical algorithms to simulate such systems. In this way the students will learn to resolve real-world problems in areas of engineering such as mechanical, aerospace, robotics, biomechanical, and mechatronics. The course provides an in-depth coverage of fundamental concepts on Newton/Euler and Lagrangian formulations for three-dimensional motions of rigid bodies and systems of rigid bodies, rotating reference frames, generalized coordinates and speeds, generalized forces, analytical and computational determination of inertia properties, Hamilton’s Principle, Kane’s method, conservation laws, holonomic and nonholonomic constraints, constraint processing, force elements for linear as well as rotational actuators, numerical integration algorithms, and computational simulation. The mathematical tools required to describe spatial motion of a rigid body will be presented in full. The subject matter is particularly relevant to applications comprised of interconnected and constrained discrete mechanical components. Computerized symbolic manipulation and time integration methods for dynamic analysis will be exercised. Although the content of the course is limited to rigid-body kinematics and dynamics, the principles can be adapted for application to more complicated problems, including those with deformable members. A solid understanding of the principles of dynamics in the context of modern analytical and computational methods is aimed.