MAE 4730 - Intermediate Dynamics

Fall. 3 credits. Letter grades only.

Prerequisite: MATH 2940, MAE 3260 or equivalents, or permission of instructor. Co-meets with MAE 5730.

A. Ruina.

The course emphasizes the classical dynamics of single- and multi-degree-of-freedom systems made up of particles, rigid-objects in 2 and 3 special dimensions. Three approaches are used: the Newton-Euler and Lagrangian approach, both using minimal coordinates, and also a ‘maximal coordinate’ approach using differential algebraic equations (DAEs). The course emphasizes finding equations of motion, solving them analytically (if possible) and numerically; and graphical presentation of solutions, including animations.

Outcome 1: Given a description in sketches and/or simple words, for a variety of dynamical mechanical systems consisting of particles and rigid objects interacting with various standard connections (e.g., strings, springs, hinges, rolling, surface sliding) and forces (e.g., gravity, friction, fluid drag), the student should be able to find the governing differential equations, solve the simple cases by hand, solve the more complex cases with numerical integration (MATLAB), graphically represent the results, including animations, and check the reasonableness of the results using extreme cases and conservations laws (momentum, angular momentum and energy).

Outcome 2: Students will be proficient at writing Lagrange equations for simple conservative systems.

Outcome 3: Students will be able to formulate, setup, numerically solve, and interpret the equations and solutions of a 3D rigid object rotating in space.