Course Objectives: To learn about the basic theory and methods of mechanical system dynamic analysis, the branch of engineering mechanics that is concerned with bodies in motion under the action of forces. This course stresses modeling of physical problems into mathematical terms, and will enable the student to model and analyze complex mechanical systems in a facile way. It will focus primarily on Kane's equations.

Course Description: The motivation for this course is twofold, first, to update and expand the student's knowledge and understanding of the modeling of mechanical systems, and second, to provide an approach that is superior to classical methods (Newton, Lagrange, and Hamilton) in that it involves simpler equations, and thereby leads to major savings in labor. This approach, Kane's equations, was developed in the early days of the modern space exploration era, when multibody spacecraft, complex robotic systems, and other complicated mechanical devices demanded more efficient ways of analysis. The major course topics comprise multibody kinematics, forces and inertia, equations of motion, and solution of the equations of motion. Multibody kinematics includes direction cosines, Euler angles, quaternions, translational velocity, angular velocity, generalized speeds, partial velocities, constraints, and holonomic and nonholonomic systems. Forces and inertia include forces, couples, torques, equivalent force systems, the inertia matrix, the inertia dyadic, generalized active forces, and generalized inertia forces. Equations of motion addresses analysis of holonomic and nonholonomic systems using Kane, Newton Euler and Lagrange approaches. Robotics and spacecraft examples will be discussed to enhance student learning and understanding.

Prerequisites: Undergraduate Dynamics

Textbook: Dynamics: Theory and Applications, by Thomas R. Kane and David A. Levinson, McGraw-Hill Publishing Company.

Grading: Homework: 10%, Midterm: 25%, Term Project: 25%, Final Exam: 40%