2020 Space Systems Analysis A

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Graduate major in Mechanical Engineering
Furuya Hiroshi 
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Course description and aims

For the dynamics of structures involved with spacecraft systems, it is important to understand the deployment characteristics of artificial satellites, large-scale space structures, deployable space structure systems, as well as their flexible, dynamic characteristics. In this lecture we will develop a mathematical treatment of multibody systems which forms the basis of dealing with them. We will cover methods for constructing a mathematical model for evaluating the mechanical characteristics of flexible structures formed from elastic bodies, as well as how to understand the dynamic characteristics of complex spacecraft structure systems.

Student learning outcomes

[Course objectives] The objective of this course is for students to gain an understanding of mathematical and mechanical methods needed for clarifying structural deformations and structural dynamics properties for lightweight, flexible spacecraft systems in a space environment. Students will also learn to apply those methods to development envelope space structures and envelope structures.
[Topic] By developing a mathematical treatment of multibody systems such as flexible structure systems and elastic deformation necessary for understanding the dynamics of spacecraft systems, students will gain an understanding of the above. We will cover mathematical approaches such as Kane's method, as well as gain an understanding of dynamics approaches to flexible space structure systems such as envelope structures.


Spacecraft systems, Multi-body systems, Flexible structures, Dynamics, Kane method

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

Aside from lectures, students will be given exercises and homework (submit as report) as necessary to deepen their understanding.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Introduction of mechanics of spacecraft system Reviewing mechanics of spacecraft system
Class 2 Basic equation of motions for spacecraft systems Understanding basic equation of motions for spacecraft systems
Class 3 Treatment of external force to spacraft systems Learn how to treat external forces working on spacecraft systems
Class 4 Dynamic properties of simple spacecraft systems Studying dynamic properties of simple spacecraft systems
Class 5 Dynamic properties of spacecraft systems with variable structures Understand how to treat the dynamic properties of spacecraft systems with variable structures
Class 6 Dynamics of thin walled structures of spacecraft systems Studying dynamics of thin walled structures of spacecraft systems
Class 7 Structural dynamics of complex spacecraft systems Understanding dynamics of complex spacecraft systems

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.


Several materials are distributed in the class.

Reference books, course materials, etc.

Dynamics: Theory and Applications, T.R. Kane, David A. Levinson
Spacecraft Dynamics, T.R. Kane, P.W. Likins, David A. Levinson

Assessment criteria and methods

Students are evaluated based on report problems from each class and the final exam. Evaluations are based on final exams (about 60%), and exercises and reports (about 40%).

Related courses

  • MEC.H432 : Multibody Systems
  • MEC.M431 : Space Systems Design
  • LAS.M102 : Linear Algebra I / Recitation
  • LAS.M106 : Linear Algebra II
  • LAS.P101 : Fundamentals of Mechanics 1
  • LAS.P102 : Fundamentals of Mechanics 2
  • MEC.B214 : Vector Analysis
  • ZUB.Q203 : Classical Mechanics

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Successful completion of learning the undergraduate level subjects listed the related courses above.
A good background in mechanics, vector analyses, and differential equations are requested.

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