Analysis

As a part of this project we were also required to analyze the behavior of the SPENDULAP under particular circumstances.

We were able to find, from the equations of motion derived, that the equilibrium , for a constant change in , is given by the following equation:

= arccos(dot^2 L / g)

We can also see that if =30 degrees at equilibrium, and the change in is constant, then it is given by the following equation, derived from manipulation of the expression above:

dot = (g cos30 / L )^.5

Giving dot = 6.73 radians/sec

Plots of (t), dot(t), and m for this situation follow in appendix A.
Plots of (t), dot(t), and m for the dot calculated above are also give for an initial angle of =45.

Appendix A

Plots at

dot = 6.73 radians/sec and

0 = 30 degrees

Plots at dot = 6.73 radians/sec and 0 = 45 degrees

Animation may be viewed by utilizing matlab files below. Execute "animate" from within Matlab to start.

animate.m
solution.m