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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 |
10.4 |
| 13 |
Generalized Coordinates, Constraints, Virtual Displacements |
4.1-4.4 |
| 15 |
Generalized Coordinates, Constraints, Virtual Displacements (cont.) |
|
| 16 |
Virtual Work, Generalized Force, Conservative Forces
Examples |
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 |
4.9 |
| 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
Example |
|
| 22 |
Linearized Equations of Motion Near Equilibria of Holonomic Systems |
5.3 |
| 23 |
Linearized Equations of Motion for Conservative Systems
Stability
Normal Modes
Mode Shapes
Natural Frequencies |
5.5 |
| 24 |
Example for Lecture 23 Topics
Orthogonality of Modes Shapes
Principal Coordinates |
5.6 |
| 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.