THE INVERTED PENDULUM AND CART SYSTEM



EQUATIONS OF MOTION: The Inverted Pendulum

p0_1

cg  =  Center of gravity
p  =  Pivot point
 
xsubcg  =  X coorordinate of center of gravity
 
xdot1cg  =  d1xcgdt First derivative of  xsubcg
 
xdot2cg  =  d2xcgdt Second derivative of  xsubcg
 
ysubcg  =  Y coorordinate of center of gravity
 
ydot1cg  =  d1ycgdt First derivative of  ysubcg
 
ydot2cg  =  d2ycgdt Second derivative of  ysubcg
 
xsubp  =  X coordinate of pivot point.
Note positive xsubp is toward right.
 
xdot1p  =  d1xpdt First derivative of  xsubp
 
xdot2p  =  d2xpdt Second derivative of  xsubp
 
ysubp  =  Y coordinate of pivot point.
 
ydot1p  =  d1ypdt First derivative of  ysubp
 
ydot2p  =  d2ypdt Second derivative of  ysubp
H  =  Force in Horizontal direction.
V  =  Force in Vertical direction.
l  =  1/2 length of pendulum
m  =  mass of pendulum
theta  =  Angle of pendulum measured from vertical.
Note positive theta is taken as clockwise.
bsubr  =  Viscous damping constant.
I  =  moment of inertia for pendulum     ( mip for uniform rod)

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