Dynamics

The course is involved with the study and description of dynamic motions of bodies subject to external forces. The kinematics of a point are developed, where the motion is studied without taking into account the forces that cause it, and the relative translational motion is studied. Next, the kinetics of point particles are studied, where the motion is related to forces through Newton/Euler laws of motion, the principles of thrust and momentum, and the principles of work and energy. Next the analysis is generalized to the kinematics of rigid bodies and the following motions are studied : translational motion, rotation around a steady axis, planar motion, rotation around steady point, general spatial motion, and relative motions with respect to rotating coordinate system. The kinetics of rigid bodies is developed through Euler equations, principles of thrust and momentum, and principles of work and energy.

Objectives

The objective is to introduce the student to the fundamental principles of dynamics of bodies. The student must understand the relation between the motion of bodies and the forces that cause the motion or developed during the motion. Also, he/she must be able to apply the basic principles of dynamics to solve practical problems with emphasis in the analysis and determination of the motion of bodies and the forces that are developed during their motion.

Prerequisites

Statics, Ordinary differential equations, Differential/Integral Calculus

Syllabus

Kinematics of particles (position, velocity, acceleration) – Motion relative to a frame in translation – Kinetics of particles (Newton’s and Euler’s laws of motion, impulse and momentum principles, work and energy principles) – Applications (impact, space mechanics) – Kinematics of rigid bodies (translational motion, rotation about a fixed axis, plane motion, motion about a fixed point, general three-dimensional motion, motion relative to a rotating frame) – Kinetics of rigid bodies (moment of inertia tensor, angular momentum and kinetic energy, Euler’s equations, impulse and momentum principles, work and energy principles) – Applications (impact, rotor balancing, axisymmetrical bodies)