| 1 |
Course Overview
Single Particle Dynamics: Linear and Angular Momentum Principles, Work-energy Principle |
(PDF) |
| 2 |
Examples of Single Particle Dynamics |
(PDF) |
| 3 |
Examples of Single Particle Dynamics (cont.) |
(PDF) |
| 4 |
Dynamics of Systems of Particles: Linear and Angular Momentum Principles, Work-energy Principle |
(PDF) |
| 5 |
Dynamics of Systems of Particles (cont.): Examples
Rigid Bodies: Degrees of Freedom |
(PDF) |
| 6 |
Translation and Rotation of Rigid Bodies
Existence of Angular Velocity Vector |
(PDF) |
| 7 |
Linear Superposition of Angular Velocities
Angular Velocity in 2D
Differentiation in Rotating Frames |
(PDF) |
| 8 |
Linear and Angular Momentum Principle for Rigid Bodies |
(PDF) |
| 9 |
Work-energy Principle for Rigid Bodies |
(PDF) |
| 10 |
Examples for Lecture 8 Topics |
(PDF) |
| 11 |
Examples for Lecture 9 Topics |
(PDF) |
| 12 |
Gyroscopes: Euler Angles, Spinning Top, Poinsot Plane, Energy Ellipsoid
Linear Stability of Stationary Gyroscope Motion |
(PDF) |
| 13 |
Generalized Coordinates, Constraints, Virtual Displacements |
(PDF) |
| 14 |
Exam 1 |
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| 15 |
Generalized Coordinates, Constraints, Virtual Displacements (cont.) |
(PDF) |
| 16 |
Virtual Work, Generalized Force, Conservative Forces
Examples |
(PDF) |
| 17 |
D'Alembert's Principle
Extended Hamilton's Principle
Principle of Least Action |
(PDF) |
| 18 |
Examples for Session 16 Topics
Lagrange's Equation of Motion |
(PDF) |
| 19 |
Examples for Session 17 Topics |
(PDF) |
| 20 |
Lagrange Multipliers, Determining Holonomic Constraint Forces, Lagrange's Equation for Nonholonomic Systems, Examples |
(PDF) |
| 21 |
Stability of Conservative Systems
Dirichlet's Theorem
Example |
(PDF) |
| 22 |
Linearized Equations of Motion Near Equilibria of Holonomic Systems |
(PDF) |
| 23 |
Linearized Equations of Motion for Conservative Systems
Stability
Normal Modes
Mode Shapes
Natural Frequencies |
(PDF) |
| 24 |
Example for Session 23 Topics
Orthogonality of Modes Shapes
Principal Coordinates |
(PDF) |
| 25 |
Damped and Forced Vibrations Near Equilibria |
(PDF) |
| 26 |
Exam 2 |
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