This page contains links to set of **notes** and **exercises** associated with a second course in rigid body dynamics. The notes cover topics relevant to two-dimensional and three-dimensional motion. A more complete presentation of three-dimensional, rigid body dynamics is provided by the 3D Dynamics eBook.

A set of exercises with answers are provided at the bottom of this page. Two of the exercises recommend practice with MATLAB/Simulink/SimMechanics®.

Trademark: MATLAB, Simulink, and SimMechanics (now called Simscape Multibody) are all registered tradmarks of The Mathworks, Inc. The Mathworks does not warrent the accuracy of the examples provided below.

#### References:

- L. Meirovitch, Methods of Analytical Dynamics, McGraw-Hill, 1970.
- T.R. Kane, P.W. Likins, and D.A. Levinson, Spacecraft Dynamics, McGraw-Hill, 1983
- T.R. Kane and D.A. Levinson, Dynamics: Theory and Application, McGraw-Hill, 1985
- R.L. Huston, Multibody Dynamics, Butterworth-Heinemann, 1990
- H. Baruh, Analytical Dynamics, McGraw-Hill, 1999
- H. Josephs and R.L. Huston, Dynamics of Mechanical Systems, CRC Press, 2002
- R.C. Hibbeler, Engineering Mechanics: Dynamics, 13th Ed., Pearson Prentice Hall, 2013
- J.L. Meriam and L.G. Craig, Engineering Mechanics: Dynamics, 3rd Ed, 1992
- F.P. Beer and E.R. Johnston, Jr. Vector Mechanics for Engineers: Dynamics, 4th Ed, 1984

#### Angular Motion and Angular Velocity

#### Derivatives in Different Reference Frames

#### Kinematics of Points Fixed on Rigid Bodies

- Relative Kinematics of Two Points Fixed on a Rigid Body
- Example System I
- Mechanical Configuration of a Robot

#### Kinematics of Points Moving on Rigid Bodies

#### Motion Constraints

- Systems with Closed Kinematic Chains
- Rolling Constraints – Point Contact
- Thrust Bearing Example
- Rolling Constraints – Line Contact
- Differential Gear Set (T.R. Kane)

#### Orientation Angles and Angular Velocity

- Orientation Angles for Rigid Bodies
- Angular Velocity and Orientation Angles
- Orientation of a Rigid Body Using Euler Parameters

#### Angular Momentum and Kinetic Energy of a Rigid Body

- Moments and Products of Inertia and the Inertia Matrix
- Angular Momentum of a Rigid Body about its Mass Center
- Angular Momentum of a Rigid Body about an Arbitrary Point
- Kinetic Energy of a Rigid Body
- Simple Crank Shaft – Angular Momentum & Kinetic Energy
- Misaligned Disk on Shaft – Angular Momentum & Kinetic Energy
- Example System II
- Example System II – Angular Momentum & Kinetic Energy

#### Newton/Euler Equations of Motion

- Newton/Euler Equations of Motion
- Bearing Loads on a Simple Crank Shaft
- Bearing Loads on a Shaft with Misaligned Disk
- Newton/Euler Equations of Motion: Example System II

#### Degrees of Freedom and Partial Velocities

- Degrees of Freedom of Mechanical Systems
- Partial Velocities and Partial Angular Velocities
- Partial Velocities and the Slider Crank Mechanism

#### Generalized Forces and the Principle of Virtual Work

#### Lagrange’s Differential Equations of Motion (Independent Generalized Coordinates)

- Introduction to Lagrangian Dynamics
- Lagrange’s Equations for Multi-Degree-of-Freedom Systems
- Lagrange’s Equations Examples (2D)
- Lagrange’s Equations: Example System II

#### Linearization of Equations of Motion, Natural Frequencies and Mode Shapes

#### Lagrange’s Equation of Motion (Dependent Generalize Coordinates)

- Configuration Constraints for Mechanical Systems
- Lagrange’s Equations for Multi-Degree-of-Freedom Systems with Dependent Generalized Coordinates
- Constraint Relaxation Method: Meaning of Lagrange Multipliers
- Example – Equations of Motion of a Slider Crank Mechanism

#### Sample Exercises with Answers

- Homework #1 Homework #1 Answers
- Homework #2A
- Homework #2B Homework #2 Answers
- Homework #3 Homework #3 Answers
- Homework #4 (MATLAB/Simulink/SimMechanics®)
- Homework #5 Homework #5 Answers
- Homework #6 Homework #6 Answers
- Homework #7 Homework #7 Answers
- Homework #8a Homework #8a Answers
- Homework #8b Homework #8b Answers
- Homework #9 (MATLAB/Simulink/SimMechanics®)
- Homework #10 Homework #10 Answers
- Homework #11 Homework #11 Answers