Reading
Assignments
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Lesson |
Textbook |
Lecture
Notes & Programs |
Comments |
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1 |
Ch. 1 | Review the "Introduction" page on this site, then review the first chapter of your textbook. This chapter is complimentary to the web-based “Introduction”. Do not be concerned about the equations that appear in this chapter. Try to understand the concepts of multibody systems and dynamics and different ways to formulate a problem. |
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2 |
Ch. 2 | Lesson 2.pdf | There are slight differences in the notations between the textbook and the PDF notes. We will follow the notation from the Notes. This is the most important lesson in this course. It provides you with the analytical tools, the notation, or simply "the language" that you need to be familiar with for multibody dynamics. By following the notation described in this lesson, you will eventually realize that multibody formulations are simple to learn and easy to manipulate. The use of this notation is a requirement in this course. If your assignemnt is prepared using a different notation, you may loose either partial or full credit for that assignment. |
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3 |
Sections 3.1, 3.1.1, 3.1.2, 3.1.3, 3.1.4, 3.1.5 | Lesson 3.pdf | ||||||||||||||||||||||
4 |
Sections 3.2, 3.2.1, 3.2.2, 3.3, 3.3.1 (briefly), 3.4, 3.4.1. 3.4.2), 12.1, 12.2.1 | Ch4_Matlab.zip | Unzip the file Ch4_Matlab and experiment with these Matlab programs in the order that are listed:
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5 |
Sections 8.1, 8.2 | Lesson 5.pdf |
Kinematics and dynamics (kinetics) of multi-particle systems are presented in these notes. The form and the derivation of equations of motion for particles are much simpler than those for rigid bodies. Therefore, understanding how the multi-particle equations are derived (and eventually solved numerically) will prepare us for the multibody equations that are more complicated. You should be able to follow the derivation of most of the material in these notes: kinematics of unconstrained and constrained multi-particle syetms, and dynamics of unconstrained multi-particle systems. However, if you are not familiar with the use of Lagrange multiplier techique, you may not understand how the equations of motion are derived for constrained multi-particle systems. This will be discussed in the class and later on in more detail when we deal with constrained multi-body systems. |
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6 |
Section 4.1 | Lesson 6.pdf | This lesson provides an overview of the kinematics of a rigid body in planar motion. This material serves as an introduction to the kinematics of a body in 3D space. |
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7 |
Section 6.1 | Lesson 7.pdf | Kinematics of a rigid body in 3D space is introduced in this lesson. Since rotation in space is analytically more complicated than the planar motion, the following several lessons are dedicated to that topic only. It is very important to comprehend analytical and physical aspects of 3D rotation. |
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8 |
Sections 6.1.1, 6.1.2, Appendix A | Lesson 8-A.pdf Lesson 8-B.pdf | This lesson introduces you to the most commonly used (not necessarily the best!) rotational coordinates in space--Euler angles and one of its conventions known as Bryant angles. |
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9 |
Sections 6.1.1, 6.1.2, 6.1.3, 6.1.4, 6.1.5, 6.2, 6.2.1 and Appendix B. | Lesson 9.pdf | This lesson introduces you to a set of rotational coordinates in space known as Euler parameters (also known as quaternions). This lesson provides you with one of the most important tools for spatial kinematics. | |||||||||||||||||||||
10 |
Sections 6.3, 6.3.1, A.1.1 and A.2.1. | Lesson 10.pdf | This lesson introduces you to the vectors of angular velocity and acceleration. You will learn about the relationships between these vectors and the first and second time derivatives of Euler parameters (and Euler angles). | |||||||||||||||||||||
11 |
Sections 7.1-7.2.4. | Lesson 11-A.pdf Lesson 11-B.pdf Lesson 11-C.pdf Lesson 11-D.pdf |
This lesson introduces you to the kinematic constraints in Body Coordinate Formulation (also called Cartesian or absolue coordinate foirmulations). | |||||||||||||||||||||
Download DAP3D (version 3.5.13 -- with universal joint) MATLAB program in zip and its User Manual in PDF. |
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12 |
Ch. 8 | This lesson introduces you to the equations of motion for a rigid body in Body Coordinate Formulation. The equations are extended to unconstrained and constrained multibody systems. | ||||||||||||||||||||||
13 |
Sections 9.2-9.2.6 | Lesson 13.pdf | This lesson introduces you to some of the commonly used force elements in multibody systems. | |||||||||||||||||||||
14 |
Sections 9.3-9.3.3 (planar systems) | Lesson 14.pdf | This lesson shows how to relate the reaction forces to the Lagrange multipliers for some of the commonly used constraints. | |||||||||||||||||||||
15 |
Lecture 3-19-20.pdf | Numerical integration of EQM in DAP3D (revised 3-22-20) | ||||||||||||||||||||||
16 |
Lecture 3-24-20.pdf | Constraint violation | ||||||||||||||||||||||
17 |
Lecture 3-26-20.pdf | Constraint violation (continued) | ||||||||||||||||||||||
18 |
Lecture 3-31-20.pdf | Rolling disk | ||||||||||||||||||||||
19 |
Lecture 4-02-20.pdf | Friction | ||||||||||||||||||||||
20
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Lecture 4-07-20.pdf | Forward and inverse dynamics with DAP3D | ||||||||||||||||||||||
21
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Lecture 4-14-20.pdf | Correcting initial conditions | ||||||||||||||||||||||
22
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Lecture 4-16-20.pdf | Joint coordinate formulation (open chain systems) (revised 4-30-20) | ||||||||||||||||||||||
23 |
Lecture 4-21-20.pdf | Joint coordinate formulation (open chain systems) (revised 4-30-20) | ||||||||||||||||||||||
24 |
Lecture 4-23-20.pdf | Joint coordinate formulation (closed chain systems) (revised 4-30-20) | ||||||||||||||||||||||
| Event.zip | A MATLAB example for the "event" function | |||||||||||||||||||||||