Due: Th 01/30
Derive the dynamic model of the inverted pendulum presented in class using your favorite method (Newton’s Laws, Lagrange’s equations, …).
Using the assumptions made in class (u = T/(mL2), g = L), perform a computer simulation of the response of the nonlinear model (S) for u = 0 and initial conditions f(0) = 0rad, df(0)/dt = 0rad/sec; f(0) = 0.15rad, df(0)/dt = 0rad/sec. Discuss your results.
Using the assumptions made in class (u = T/(mL2), g = L), perform a computer simulation of the response of the linear model (S*) for u = 0 and initial conditions f(0) = 0rad, df(0)/dt = 0rad/sec; f(0) = 0.15rad, df(0)/dt = 0rad/sec. Discuss your results and compare to those of question 2.
Analytically solve the linear model (S*) for f(t) using your favorite method (integrating factor, separation, Laplace Transforms, …) when u = 0 and f(0) = 0.15rad, df(0)/dt = 0rad/sec. Does this match your simulated response in question 3?