Professor Oliver M. O'Reilly

Department of Mechanical Engineering

University of California at Berkeley

*This course is an introduction to the dynamics of particles and rigid bodies. The material, based on a Newtonian formulation of the governing equations, is illustrated with numerous examples ranging from one-dimensional motion of a single particle to planar motions of rigid bodies and systems of rigid bodies.*

This was the first course Professor O'Reilly taught when he joined the U.C. Berkeley faculty in the Fall of 1992 and he has enjoyed teaching it many times since then. He typically uses his textbook - shown on the right - for lecture material. The homework problems for this course are assigned from a standard engineering dynamics textbook and are supplemented with computational components

*This course builds upon material learned in 104, examining the dynamics of particles and rigid bodies moving in three dimensions. Topics include non-fixed axis rotations of rigid bodies, Euler angles and parameters, kinematics of rigid bodies, and the Newton-Euler equations of motion for rigid bodies. The course material will be illustrated with real-world examples such as gyroscopes, spinning tops, vehicles, and satellites. Applications of the material range from vehicle navigation to celestial mechanics, numerical simulations, and animations.*

*This course introduces and investigates Lagrange's equations of motion for particles and rigid bodies. The subject matter is particularly relevant to applications comprised of interconnected and constrained discrete mechanical components. The material is illustrated with numerous examples. These range from one-dimensional motion of a single particle to three-dimensional motions of rigid bodies and systems of rigid bodies.*

What is novel about the treatment of Lagrange's equations in this course is the emphasis placed on differential geometry. This enables the student to see the equivalence between Lagrange's equations of motion with the Newton-Euler equations of motion. Professor O'Reilly has also found that the material on rotations and curvilinear coordinate systems in this course are among the most useful topics that he teaches. This course's instruction is based off of another of Professor O'Reilly's books - seen above in English (found here) and at right in a Russian translation (found here).

*Review of Lagrangian dynamics. Legendre transform and Hamilton's equations, Cyclic coordinates, Canonical transformations, Hamilton-Jacobi theory, integrability. Dynamics of asymmetric systems. Approximation theory. Current topics in analytical dynamics.*

This course is considered by Professor O'Reilly to be a synthesis of the ME104-ME170-ME175 sequence of courses on particle and rigid body dynamics with material on vibrations from ME273-ME277. The first half of the course is devoted to Lagrange's equations of motion for mechanical systems and an examination of the stability and bifurcations of equilibria and steady motions (relative equilibria). In the second half of the course, canonical and non-canonical forms of Hamilton's equations of motion are introduced and illustrated using a range of examples drawn from the mechanics of rigid bodies and celestial mechanics.

This is a collaborative online resource created by Professor O'Reilly and Alyssa Novelia of UC Berkeley and Assistant Professor Daniel T. Kawano of the Rose–Hulman Institute of Technology. The resource contains instructional materials featuring rotations of rigid bodies in three dimensions. Simulations, animations, and historical commentary are also provided. The applications are wide spread and include rigid body dynamics, inertial navigation, celestial mechanics, video games, and orthopaedic biomechanics, among many others.

The complete educational resource may be viewed at rotations.berkeley.edu; a sampling of the most recently updated sections of this resource are featured below: