Lecture Notes

All 24 lecture notes are courtesy of Mohammad-Reza Alam. Used with permission.

LEC # TOPICS LECTURE NOTES
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
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