This page contains links to set of notes, example problems, 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 in 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 trademarks of The MathWorks, Inc. The MathWorks does not warrant 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
Kinematics of Points Moving on Rigid Bodies
Orientation Angles and Angular Velocity
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
Degrees of Freedom and Partial Velocities
Generalized Forces and the Principle of Virtual Work
Lagrange’s Differential Equations of Motion
(Independent Generalized Coordinates)
Linearization of Equations of Motion, Natural Frequencies and Mode Shapes
Lagrange’s Equation of Motion
(Dependent Generalized Coordinates)
Example Problems
- Example #1 – Angular Velocity and Angular Acceleration
- Example #2a – Calculation of Velocity using Direct Differentiation
- Example #2b – Calculation of Velocity using the Derivative Rule
- Example #3 – Calculation of Acceleration using the Derivative Rule
- Example #4 – Calculation of Velocity using the Two-Point Formula
- Example #5 – Calculation of Acceleration using the Two-Point Formula
- Example #6 – Calculation of Velocity and Acceleration using the Formulae for a Point Moving on a Body
- Example #7 – Calculation of Velocity using the Formula for a Point Moving on a Body
- Example #8 – Calculation of Acceleration using Formula for a Point Moving on a Body
- Example #9 – Calculation of Velocity using the Formula for a Point Moving on a Body
- Example #10 – Calculation of Acceleration using the Formula for a Point Moving on a Body
- Example #11 – Angular Momentum & Kinetic Energy of a Simple Crank Shaft
- Example #12 – Angular Momentum & Kinetic Energy of a Misaligned Disk
- Example #13 – Angular Momentum & Kinetic Energy of a Two DOF System
- Example #14 – Bearing Loads on a Simple Crank Shaft
- Example #15 – Bearing Loads on a Misaligned Disk
- Example #16 – Newton Equations of Motion for a Two DOF System
- Example #17 – Partial Velocities for a Slider-Crank Mechanism
- Example #18 – Principle of Virtual Work (Simple Mechanism)
- Example #19 – Principle of Virtual Work (Simple Mechanism)
- Example #20 – Lagrange’s Equations (1 DOF system)
- Example #21 – Lagrange’s Equations (2 DOF system)
- Example #22 – Lagrange’s Equations (2 DOF system)
- Example #23 – Lagrange’s Equations (3D, 2 DOF system)
- Example #24 – Linearization of Equations of Motion
- Example #25 – Linearization of Equations of Motion
- Example #26 – Natural Frequencies and Mode Shapes
Exercises
- Exercises #1 (Exercises #1 Answers)
- Exercises #2A
- Exercises #2B (Exercises #2 Combined Answers)
- Exercises #3 (Exercises #3 Answers)
- Exercises #4 (MATLAB, Simulink/SimMechanics® Modeling)
- Exercises #5 (Exercises #5 Answers)
- Exercises #6 (Exercises #6 Answers)
- Exercises #7 (Exercises #7 Answers)
- Exercises #8a (Exercises #8a Answers)
- Exercises #8b (Exercises #8b Answers)
- Exercises #9 (MATLAB/Simulink/SimMechanics®)
- Exercises #10 (Exercises #10 Answers)
- Exercises #11 (Exercises #11 Answers)