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Lecture Notes



Lecture Notes

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

LEC #TOPICSLECTURE NOTES
1Course Overview

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

Rigid Bodies: Degrees of Freedom
(PDF)
6Translation and Rotation of Rigid Bodies

Existence of Angular Velocity Vector
(PDF)
7Linear Superposition of Angular Velocities

Angular Velocity in 2D

Differentiation in Rotating Frames
(PDF)
8Linear and Angular Momentum Principle for Rigid Bodies(PDF)
9Work-energy Principle for Rigid Bodies(PDF)
10Examples for Lecture 8 Topics(PDF)
11Examples for Lecture 9 Topics(PDF)
12Gyroscopes: Euler Angles, Spinning Top, Poinsot Plane, Energy Ellipsoid

Linear Stability of Stationary Gyroscope Motion
(PDF)
13Generalized Coordinates, Constraints, Virtual Displacements(PDF)
14Exam 1
15Generalized Coordinates, Constraints, Virtual Displacements (cont.)(PDF)
16Virtual Work, Generalized Force, Conservative Forces

Examples
(PDF)
17D'Alembert's Principle

Extended Hamilton's Principle

Principle of Least Action
(PDF)
18Examples for Session 16 Topics

Lagrange's Equation of Motion
(PDF)
19Examples for Session 17 Topics(PDF)
20Lagrange Multipliers, Determining Holonomic Constraint Forces, Lagrange's Equation for Nonholonomic Systems, Examples(PDF)
21Stability of Conservative Systems

Dirichlet's Theorem

Example
(PDF)
22Linearized Equations of Motion Near Equilibria of Holonomic Systems(PDF)
23Linearized Equations of Motion for Conservative Systems

Stability

Normal Modes

Mode Shapes

Natural Frequencies
(PDF)
24Example for Session 23 Topics

Orthogonality of Modes Shapes

Principal Coordinates
(PDF)
25Damped and Forced Vibrations Near Equilibria(PDF)
26Exam 2

 








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