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# Orbital Perturbations

In practice the resulting expressions are truncated to allow simpler expressions in the theory. This trade-off speeds up computation but decreases accuracy. Unlike numerical techniques, analytical methods produce approximate or 'general' results that hold for some limited time interval and accept any initial input conditions. The quality of the solution degrades over time, but so does the numerical solution at different rates and for different reasons. Analytical techniques are generally more difficult to develop than numerical techniques, but they often lead to a better understanding of the perturbation source.

## AAE69000

3

### Learning Objective:

The main focus of the course will be on general perturbation techniques in orbital mechanics. General perturbation techniques replace the original equations of motion with an analytical approximation that captures the essential character of the motion over some limited time interval and which permits analytical integration. Such methods usually rely on series expansions of the perturbing accelerations.

### Description:

In practice the resulting expressions are truncated to allow simpler expressions in the theory. This trade-off speeds up computation but decreases accuracy. Unlike numerical techniques, analytical methods produce approximate or 'general' results that hold for some limited time interval and accept any initial input conditions. The quality of the solution degrades over time, but so does the numerical solution at different rates and for different reasons. Analytical techniques are generally more difficult to develop than numerical techniques, but they often lead to a better understanding of the perturbation source.

### Topics Covered:

n-Body Problem, Theory of Perturbations, Applications of Orbital Perturbations, The Method of Averaging, Effects of Relativity, Perturbations due to Drag, Periodic Solutions in Nonlinear Oscillations

### Prerequisites:

Must have bachelor degree in engineering or related field.

### Applied / Theory:

30 / 70

https://mycourses.purdue.edu

### Web Content:

Syllabus, grades, lecture notes, homework assignments, solutions, and quizzes.

### Homework:

75% of grade based on student's journal, turned in approximately every 2 weeks for grading. Homework submitted via Blackboard or emailed to instructor.

### Projects:

Required. 25% of the grade will be based on a written term paper to be turned in near the end of the semester. The final project should have significant mathematical content, but it should be fun also. The types of topics allowed and encouraged include: biographies, tutorials, history, reviews of journal articles or book chapters, simulations, and mathematical analyses.

### Exams:

No exams for this course.

### Textbooks:

Official textbook information is now listed in the Schedule of Classes. NOTE: Textbook information is subject to be changed at any time at the discretion of the faculty member. If you have questions or concerns please contact the academic department.
Tentative: No required text. Course notes and a list of references will be provided.

### Computer Requirements:

ProEd Minimum Computer Requirements

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