Spring Pendulum Dynamic System - Mechatronics

O
de
r
dθ
de
θ
dθ
Mechatronics
Spring-Pendulum Dynamic System
Polar Coordinates:
Position, Velocity, Acceleration
= e
=−e
θ
θ
r
r
e θ
e r
PATH
r
v
a
r
= re
r
dr
= = re
r
+ rθ eθ = vrer
+ vθeθ
dt
dv
= = c r− rθ h b e r
+ r + r e
dt
g
2
θ 2 θ
= ae
+ ae
r
θ
r
θ+
r
θ
rθ
2
r
r
magnitude change
direction change
magnitude change
direction change
θ
θ
K. Craig
6
v r
θ
v θ