- #1
Robben
- 166
- 2
Homework Statement
For a double pendulum, how do we plot the phase space for ##\theta_2## (the lower of the pendulum), i.e. the plot ##\theta_2, \ \dot{\theta}_2?##
- ##x## = horizontal position of pendulum mass
- ##y## = vertical position of pendulum mass
- ##\theta## = angle of pendulum (0 = vertical downwards, counter-clockwise is positive)
- ##L## = length of rod (constant)
Homework Equations
F = ma
##x_1 = L_1\sin \theta_1##
##y_1 = L_1\cos \theta_1##
(the ##_1## subscript is the upper pendulum while ##_2## is the lower pendulum)
The Attempt at a Solution
I found the equation for ##\theta''_2## (which is pretty long to write in here, but I will write if you guys want me to) and I converted the second order equation into a first order, by substituting ##\theta''_2## to ##\omega'_2##, i.e. ##\omega'_2 = \theta''_2##, but I am wondering what exactly is ##\theta_2## suppose to be here?
Will our ##\theta_2## just be the ##\theta_2## in ##x_2 = x_1 + L_2 \sin\theta_2##?