Chapter 8.6, Problem 6E

Interpretation Introduction

Interpretation:

To explain the Lissajous figures and interpret them for the given system of differential equations.

• (a) To show that for given solutions $\text{x = A(t)sinθ(t), y = B(t)sin}\varphi \text{(t)}$ of the system,

  $\dot{\text{A}}\text{ = }\dot{\text{B}}\text{ = 0}$ and $\dot{\text{θ}}\text{ = 1 and }\dot{\text{θ}}\text{ = ω}$

• (b) To explain why (a) means that the trajectories are typically confined to the two-dimensional tori in four-dimensional phase space.

• (c) To explain how the Lissajous figures relate the trajectories of the system.

Concept Introduction:

• ➢ Lissajous figures are two independent oscillators plotted against each other. They are useful to visualize the knots and quasiperiodicity.