The course will be based on the material presented in the lectures. There is no required textbook, although the following books are recommended.

Baruh, H. Analytical Dynamics. New York, NY: McGraw-Hill, 1998. ISBN: 9780073659770.

Ginsberg, J. H. Advanced Engineering Dynamics. 2nd ed. Cambridge, UK: Cambridge University Press, 1995. ISBN: 9780521470216.

Crandall, S. H., D. C. Karnopp, E. F. Kurtz, Jr., and D. C. Pridmore-Brown. Dynamics of Mechanical and Electromechanical Systems. Malabar, FL: Krieger, 1982. ISBN: 9780898745290.

Moon, F. C. Applied Dynamics. New York, NY: Wiley, 1998. ISBN: 9780471138280.

Greenwood, D. T. Classical Dynamics. New York, NY: Dover Publications, 1997. ISBN: 9780486696904.

———. Principles of Dynamics. Upper Saddle River, NJ: Prentice-Hall, 1987. ISBN: 9780137099818.

Suggested Readings

The following table lists sample readings, by lecture session, from Baruh's Analytical Dynamics.

1 Course Overview

Single Particle Dynamics: Linear and Angular Momentum Principles, Work-energy Principle
1.4, 1.6, 1.7
2 Examples of Single Particle Dynamics
3 Examples of Single Particle Dynamics (cont.)
4 Dynamics of Systems of Particles: Linear and Angular Momentum Principles, Work-energy Principle 3.1-3.4
5 Dynamics of Systems of Particles (cont.): Examples

Rigid Bodies: Degrees of Freedom
6.1, 6.2, 7.1, 7.2, 1.5
6 Translation and Rotation of Rigid Bodies

Existence of Angular Velocity Vector
2.4, 2.5
7 Linear Superposition of Angular Velocities

Angular Velocity in 2D

Differentiation in Rotating Frames
2.4, 2.5, 2.6
8 Linear and Angular Momentum Principle for Rigid Bodies 8.1, 8.2
9 Work-energy Principle for Rigid Bodies 8.9
10 Examples for Lecture 8 Topics
11 Examples for Lecture 9 Topics
12 Gyroscopes: Euler Angles, Spinning Top, Poinsot Plane, Energy Ellipsoid

Linear Stability of Stationary Gyroscope Motion
13 Generalized Coordinates, Constraints, Virtual Displacements 4.1-4.4
15 Generalized Coordinates, Constraints, Virtual Displacements (cont.)
16 Virtual Work, Generalized Force, Conservative Forces

4.4, 4.5
17 D'Alembert's Principle

Extended Hamilton's Principle

Principle of Least Action
4.7, 4.8
18 Examples for Lecture 16 Topics

Lagrange's Equation of Motion
19 Examples for Lecture 17 Topics
20 Lagrange Multipliers, Determining Holonomic Constraint Forces, Lagrange's Equation for Nonholonomic Systems, Examples 4.10
21 Stability of Conservative Systems

Dirichlet's Theorem

22 Linearized Equations of Motion Near Equilibria of Holonomic Systems 5.3
23 Linearized Equations of Motion for Conservative Systems


Normal Modes

Mode Shapes

Natural Frequencies
24 Example for Lecture 23 Topics

Orthogonality of Modes Shapes

Principal Coordinates
25 Damped and Forced Vibrations Near Equilibria 5.7

Other References

Goldstein, H. Classical Mechanics. Cambridge, MA: Addison-Wesley, 1959.

Hartog, J. P. Den. Mechanics. New York: Dover, 1961.

Marion, J. B. Classical Dynamics of Particles and Systems. 2nd ed. New York: Academic Press, 1970.

Landau, L. D., and E. M. Lifshitz. Mechanics. 3rd ed. New York: Pergamon, 1976.

Williams, J. H., Jr. Fundamentals of Applied Dynamics. New York: John Wiley, 1996.

Hartog, J. P. Den. Mechanical Vibrations. New York: McGraw-Hill, 1956.

Meirovitch, L. Elements of Vibration Analysis. New York: McGraw-Hill, 1975.

———. Analytical Methods in Vibrations. New York: Macmillan, 1967.

Pippard, A. B. Response and Stability. New York: Cambridge University Press, 1985.

Nayfeh, A. H., and D.T. Mook. Nonlinear Oscillations. New York: Wiley-Interscience, 1979.

Strogatz, S. H. Nonlinear Dynamics and Chaos. Reading, MA: Addison-Wesley, 1994.