THE FREE HANGING PENDULUM



EQUATIONS OF MOTION: The Free Hanging Pendulum



cg  =  Center of gravity
p  =  Pivot point
 
 =  X coorordinate of center of gravity
 
 =    First derivative of 
 
 =    Second derivative of 
 
 =  Y coorordinate of center of gravity
 
 =    First derivative of 
 
 =    Second derivative of 
 
 =  X coordinate of pivot point.
Note positive is toward right.
 
 =    First derivative of 
 
 =    Second derivative of 
 
 =  Y coordinate of pivot point.
 
 =    First derivative of 
 
 =    Second derivative of 
 
H  =  Force in Horizontal direction.
V  =  Force in Vertical direction.
 =  1/2 length of pendulum
m  =  mass of pendulum
 =  Angle of pendulum measured from vertical.
Note positive is taken as clockwise.
 =  Viscous damping constant.
I  =  moment of intertia for pendulum     ( for uniform rod)

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