Lecture on Parametric Curves and MATLAB

Introduction to Parametric Curves

• Also known as vector-valued functions.
• Explore using MATLAB for visualization.
• Not part of APS-C 171 curriculum, but useful for programming experience.

MATLAB Introduction

• MATLAB is free for Queen's students.
• Download via ITS software center.

Running a MATLAB Script

• Initial example involves plotting using cos(t) and sin(t).
• Use of axis equal command to maintain equal proportions on x and y axes.
• Example produces a circle by plotting parametric equations.

Understanding MATLAB Code

• Define range for t from 0 to 2π with a step of 0.01.
• Plot with cos(t) for x-values and sin(t) for y-values.
• Demonstrates creating a smooth circle.

Animation in MATLAB

• Aims to show trajectory over time.
• Use of a for loop to iterate over time values.
• Plotting individual points over time to demonstrate movement.

Improving Visibility in MATLAB

• Change marker size to make points visible.
• Use close all to reset graphics windows.
• drawnow command enables animation effect.
• Control plot window visibility and order with plotting commands.

Enhancing Animation

• Use CLF to clear figure and hold on to retain previous plots.
• Plot entire trajectory with a distinct path and moving dot.
• Adjust speed by changing time point intervals (e.g., every 10th point).
• Demonstrate multiple loops around the circle by extending t range.

Concepts of Parametric Graphing

• Difference from traditional xy graphs: involves time as a parameter.
• Each point on the graph relates to a specific time value.
• Important to consider direction of travel and maximum reach in x and y as functions of time.
• Relevant for interpreting particle trajectories.