4.2 Galileo Pendulum
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Fig. 4.7 Galileo pendulum
Fig. 4.8 State diagram of
the Galileo pendulum model
write the physical formulation of the problem: we divide the motion of the Galilean
mathematical pendulum into two stages.
We describe the mathematical model of this system in the form of a state diagram
(Fig. 4.8).
The first stage is the movement of the pendulum to the left of the equilibrium
position θ < 0. We write down the equation of motion of a mathematical pendulum
in the field of gravity already known to us. We know that at this stage the pendulum
oscillates at full suspension:
d
2
θ
dt 2 = −
g
L
sin θ
or, reducing to first-order equations:
dθ
dt
= ω
dω
dt
= −
g
l
sin θ
In software implementation:
der(theta) = omega;
if theta < 0 then
der(omega) = -g / l * sin(theta);