WOLFRAM|DEMONSTRATIONS PROJECT

Spinning Disk Pendulum Swinging on Top of a Rotating Table

​
min
max
len
10
min
max
ρ
m
10
min
max
ρ
M
1
min
max
r
6.
min
max
R
20.
min
max
h
5.
min
max
H
5.
min
mid
θ
133
min
mid
ψ
186
min
mid
ϕ
112
min
max
•
θ
0.4
min
max
•
ψ
0.2
min
max
•
ϕ
0.3
step size
0.025
run
viewpoint
1
2
3
4
5
6
7
8
display
bob only
test
0
time (sec)
000000
θ
ψ
ϕ
P.E. (kJ)
K.E. (kJ)
position (deg)
133.000
186.000
112.000
00000932.
00004813.
ω (hz)
+00.400
+00.200
+00.300
16.0 %
84.0 %
I =
00628161.5
0
0
0
00628161.5
0
0
0
00101787.6
ω =
0000000002.9
L =
0001800646.7

dL
dt
 =
0003625759.6
ω =
(
+00000002.5
+00000001.4
-00000000.0
)
L = Iω =
(
+001578741.9
+000865964.1
-000002941.6
)
dL
dt
=
(
-003146776.4
+001801091.4
+0000000000
)
zoom
info
box
trace
length
thickness
This Demonstration shows a pendulum with a small spinning rigid cylindrical bob in which the pendulum rod (assumed to have negligible mass) swings from a frame fixed on top of a rotating table. The system has three degrees of freedom: the pendulum swing angle
θ
, the spin angle
ψ
of the pendulum bob, and the rotation angle
ϕ
of the large table.
The angular momentum
L
of the bob with reference to a fixed point in space and the bob's absolute rate of angular momentum change
dL
dt
are calculated and displayed in vector form.
The instantaneous values of the system's kinetic and potential energy (red and blue bars, respectively) are shown graphically. Other options are available to help study further details of this system.
The program was constructed by finding the Lagrangian, deriving the three nonlinear equations of motion and solving them numerically.
The principal moments of inertia are used for the bob. The fixed point in space that was used to calculate
L
is the point where the pendulum rod is attached to the frame.