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Assignments


Lesson 
Textbook 
Lecture
Notes & Programs 
Comments 

1 
Ch. 1  Review the "Introduction" page on this site, then review the first chapter of your textbook. This chapter is complimentary to the webbased “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. 

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 for multibody dynamics. By following the notation described in this lesson, you will eventually find that multibody formulations to be simple 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. 

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:


5 
Sections 8.1, 8.2  Lesson 5.pdf 
Kinematics and dynamics (kinetics) of multiparticle 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 multiparticle 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 multiparticle syetms, and dynamics of unconstrained multiparticle 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 multiparticle systems. This will be discussed in the class and later on in more detail when we deal with constrained multibody systems. 

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. 

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. 

8 
Sections 6.1.1, 6.1.2, Appendix A  Lesson 8A.pdf Lesson 8B.pdf  This lesson introduces you to the most commonly used (not necessarily the best!) rotational coordinates in spaceEuler angles and one of its conventions known as Bryant angles. 

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 7.17.2.4.  Lesson 11A.pdf Lesson 11B.pdf Lesson 11C.pdf Lesson 11D.pdf 
This lesson introduces you to the kinematic constraints in Body Coordinate Formulation (also called Cartesian or absolue coordinate foirmulations).  
Download DAP3D (version 3.5.11) program (MATLAB). The User Manual in PDF is also included. (Revised 02/19/18) 

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 9.29.2.6  Lesson 13.pdf  This lesson introduces you to some of the commonly used force elements in multibody systems.  
14 
Sections 9.39.3.3 (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.  
16 
Lesson 16.pdf  Coordinate transformation  
FrictionContact.pdf  Modeling friction  
Event.zip  A MATLAB example for the "event" function  
17 
Lesson 17.pdf  Joint coordinate (openchain)  
18 
Lesson 18.pdf  Joint coordinate (closedchain)  
Impact.pdf  
19  Rolling disk.pdf  
20 
Point_Coord.pdf  Point coordinate 