Project 1

Project 1: [click here]

Due: Oct 28 (Friday) 1159pm

Submit only the final PDF file.

Lecture 9 (Sep 29)

Attractor. Basin of attraction.

Damped-driven pendulum. Poincare section.

Movies:

• Overdamped-undriven: [click here]
• Underdamped-undriven: [click here]
• Damped-driven pendulum for f=1.5, gamma=2/3:
• q=1.24: period-1 motion [click here]
• q=1.36: period-2 motion [click here]
• q=1.3725: period-4 motion [click here]
• q=1.3741: period-8 motion [click here]
• Poincare section for f=1.5, gamma=2/3 and q=4 with solutions at t=[10001:50000]*2pi/gamma: [click here] (computational time is around 2 mins).

Lecture 8 (Sep 27)

Linear stability analysis.

Lecture 7 (Sep 22)

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

Simplification II: linear driven pendulum.

Simplification III: linear damped-driven pendulum.

Simplification IV: Nonlinear damped-undriven pendulum.

Lecture 6 (Sep 20)

Model for damped-driven nonlinear pendulum.

Dimensional analysis.

Non-dimensionalization.

Reference
The Physical Basis of dimensional analysis - A.Solin

Lecture 5 (Sep 15)

Lecture cancelled.

Lecture 4 (Sep 13)

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

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

MATLAB demonstration for ODE solvers: [click here]

NOTE: In the lecture, I mentioned that HW1 will due Sep 30. But it should be Sep 23 (NEXT FRIDAY) as stated on the blog and the question paper. This leaves you two weeks between the deadlines of HW4 and Project 1 (which will due Oct 28).

HW1-4

HW1: Due 23 Sep
HW2: Due 30 Sep
HW3: Due 7 Oct
HW4: Due 14 Oct

We will have one more set of HW due near the end of the course.

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.

Lecture 2 (Sep 6)

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.

Lecture 1 (Sep 1)

Course overview

PPT slides: [click here]

Reference
Scientific computing - J. Chasnov