Lecture 9 (Sep 29)

Poincare Section

PPT: [click here]

Project 1

Section 2.17: #1

Due: Oct 29 (Sunday) 1159pm

Submit only the final PDF file.

HW3

HW:
Chapter 2.16: #6, 7
Deadline: Oct 6 (Friday) 11:59pm

Lecture 8 (Sep 25)

Limit cycle

Attractor

Basin of attraction

PPT: [click here]

Lecture 7 (Sep 22)

Linear stability analysis.

PPT: [click here]

Lecture 6 (Sep 18)

Simplification I: linear damped pendulum. Under-damped, over-damped, critically-damped. Phase diagram.

Simplification II: linear driven pendulum.

Simplification III: Nonlinear damped pendulum.

Linear stability analysis.

PPT: [click here]

Note: [click here]

HW2

HW:
Chapter 2.16: #3, 4, 5
Deadline: 29 Sep (Friday) 11:59pm

Lecture 5 (Sep 15)

Model for damped-driven nonlinear pendulum.

Dimensional analysis.

Non-dimensionalization.

PPT: [click here]

HW1

HW:
Chapter 2.16: #1, 2
Deadline: 22 Sep (Friday) 11:59pm

Lecture 4 (Sep 11)

The forward Euler method and the Runge-Kutta methods for solving an ODE.

MATLAB demonstration for ODE solvers: [click here]

PPT: [click here]

HW:
Chapter 2.16: #1, 2
Deadline: 22 Sep (Friday) 11:59pm

Lecture 3 (Sep 8)

Approximation of the period of the nonlinear undamped-undriven pendulum system.

Phase space. Phase diagram or Phase portrait of the linear and nonlinear pendulum.

PPT: [click here]

Lecture 2 (Sep 4)

Introduction to Mathematical Modeling

4 steps in doing modeling:
1. formulation of a problem: approximations and assumptions to develop, simplify and understanding the mathematical model;
2. solve the equation(s): analytically (usually with some simplification) and numerically;
3. interpretation of the mathematical results in the context of the physical problem;
4. prediction: see the limitation(s) of the mathematical model/theory.

Simple pendulum: derivation of the nonlinear ODE. small angle approximation. period for both the linear and nonlinear pendulum.

PPT: [click here]

Lecture 1 (Sep 1)

Introduction [pdf]