AME Undergraduate Courses

AME 30381: Orbital and Space Dynamics

CATALOG DATA:
The one- and two-body problems: geometrical elements and time dependence. Orbital determination. Linear orbits and regularization. Orbital transfer. The n-body problem: various forms of the three-body problem, including the circular restricted case, its "equilibrium" solutions and their stability.

Prerequisites: AME 20222

TEXTBOOK:
Fundamentals of Astrodynamics; Bake, Mueller and White

COURSE OBJECTIVES :
Upon competion of this course a student should be able to:

develop the dynamic model, or equations of motion, which approximate the motion of orbiting bodies using Newton's second law;

discuss and explain the ramifications and purpose of the assumptions and simplifications involved in the development of the approximate dynamic models;

analytically solve the dynamic model for the classical two-body problem;

numerically solve the dynamic model for systems with more than two bodies using numerical integration;

numerically solve various problems using iteration techniques and computer software;

generate plots and animations using computer software in order to visualize and interpret the behavior predicted by the analytical and numerical solutions.

TOPICS COVERED:

Generalized Coordinates and degrees-of-freedom including orbital elements and orbit determination.

Spatial Kinematics - Geometric descriptions of position and orientation using astronomical and other coordinate systems.

Newton's second law applied to approximating the motion of bodies acted on by a central force.

Analytical solution of the equations of motion for the two-body problem. This includes angular momentum and the conic sections, especially the ellipse in Cartesian and polar coordinates which is the trajectory equation.

The ballistic missile problem.

The rocket equation.

In-plane and out-of-plane orbital manuevers including the Hohmann transfer.

Introduction to the three- and n-body Problems.

Orbital period and time of flight

SCHEDULE:
Course meets three times a week for 50 minutes or twice a week for 75 minutes

CONTRIBUTION TO THE PROFESSIONAL COMPONENT:
This course represents a balance between engineering science and design, with approximately 67% engineering science and 33% design.

CONTRIBUTION TO PROGRAM LEARNING OUTCOMES AND ASSESSMENT :

Outcome criterion

Topic

Student’s previous
knowledge

Direct measures of
outcome

e

Be able to develop the dynamic model, or equations of motion, which approximate the motion of orbiting bodies using Newton's second law

Newton's second law

Homework \#4 and First Exam

b

Be able to analytically solve the dynamic model for
the classical two-body problem.

Differential equations

Second Exam

b

Be able to numerically solve the dynamic model for
systems with more than two bodies using numerical integration.

Computer programming

Homework \#6 and several homeworks after.

Prepared by: Alan P. Bowling, June 6, 2006

Direct comments, questions, and corrections to amedept@nd.edu

Outcome criterion	Topic	Student’s previous knowledge	Direct measures of outcome
e	Be able to develop the dynamic model, or equations of motion, which approximate the motion of orbiting bodies using Newton's second law	Newton's second law	Homework \#4 and First Exam
b	Be able to analytically solve the dynamic model for the classical two-body problem.	Differential equations	Second Exam
b	Be able to numerically solve the dynamic model for systems with more than two bodies using numerical integration.	Computer programming	Homework \#6 and several homeworks after.