Rigid Body Pendulum on a Flywheel

rod length (m)

7.5

mass of rod (kg)

3.5

mass of flywheel (kg)

3.5

θ(0) (deg)

45

ϕ(0) (deg)

90

θ'(0) (deg/sec)

24

ϕ'(0) (deg/sec)

50

animate rate

2.

start simulation

select viewpoint

1

2

3

4

5

6

7

time (sec)	θ (deg)	ϕ (deg)
0100.00	+017.23	240.62

This Demonstration simulates the motion of a rigid pendulum pivoted, with no friction, to a rotating flywheel. The pendulum is forced to spin on its axes by the flywheel's angular motion and at the same it can swing in a fixed 2D plane. The system has two degrees of freedom:

θ

, which is the pendulum's swing angle, and

ϕ

, which is the flywheel's rotation angle. The two nonlinear equations of motion are derived using the Lagrangian energy method. The two equations are solved numerically and the motion is simulated. Interesting motion profiles can be observed by changing the system parameters and the initial conditions.