# Calendar

LEC # TOPICS KEY DATES
1 Course Overview

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

Rigid Bodies: Degrees of Freedom
Problem set 1 due
6 Translation and Rotation of Rigid Bodies

Existence of Angular Velocity Vector
7 Linear Superposition of Angular Velocities

Angular Velocity in 2D

Differentiation in Rotating Frames
Problem set 2 due
8 Linear and Angular Momentum Principle for Rigid Bodies
9 Work-energy Principle for Rigid Bodies Problem set 3 due
10 Examples for Lecture 8 Topics
11 Examples for Lecture 9 Topics Problem set 4 due
12 Gyroscopes: Euler Angles, Spinning Top, Poinsot Plane, Energy Ellipsoid

Linear Stability of Stationary Gyroscope Motion
13 Generalized Coordinates, Constraints, Virtual Displacements Problem set 5 due
14 Exam 1
15 Generalized Coordinates, Constraints, Virtual Displacements (cont.)
16 Virtual Work, Generalized Force, Conservative Forces

Examples
17 D'Alembert's Principle

Extended Hamilton's Principle

Principle of Least Action
Problem set 6 due
18 Examples for Lecture 16 Topics

Lagrange's Equation of Motion
19 Examples for Lecture 17 Topics Problem set 7 due
20 Lagrange Multipliers, Determining Holonomic Constraint Forces, Lagrange's Equation for Nonholonomic Systems, Examples Problem set 8 due
21 Stability of Conservative Systems

Dirichlet's Theorem

Example
22 Linearized Equations of Motion Near Equilibria of Holonomic Systems Problem set 9 due
23 Linearized Equations of Motion for Conservative Systems

Stability

Normal Modes

Mode Shapes

Natural Frequencies
24 Examples for Lecture 23 Topics

Orthogonality of Modes Shapes

Principal Coordinates
Problem set 10 due
25 Damped and Forced Vibrations Near Equilibria
26 Exam 2