Why is potential energy considered negative in an inversed pendulum system?

[Andrax]

we have an inversed pendulum(ignore the car)

and we choose the coordinate system to be upwards
the potential energy PE=mgz (z will be hegative since( O,k) is upwards right?) z is always under O.
but in the textbook they basically take the absolute value of h i don't understand why?

 

[ModusPwnd]

Where is the textbook putting the zero of h?

 

[Andrax]

Where is the textbook putting the zero of h?

at the point of rest of the pendulum (same as O)

 

[Andrax]

fixed the problem (h ad to do with angle being negatgive which means the work of p is negative)
sorry my explication of the question was off , close this thread

 

[PJC01]

I would clarify that potential energy is a relative quantity, meaning it can only be measured in comparison to a reference point. In the case of an inverted pendulum, the reference point is typically chosen to be the lowest point of the pendulum, where the potential energy is considered to be zero. This means that as the pendulum moves upwards, the potential energy increases and becomes positive. However, if we choose a different reference point, for example the highest point of the pendulum, then the potential energy would be negative at the lowest point and decrease as the pendulum moves upwards.

The reason why the textbook may take the absolute value of the height is to simplify the calculations and avoid dealing with negative values. It is important to note that the magnitude of the potential energy is what matters in determining the behavior of the system, rather than its sign. So whether we use the absolute value or not, the physical principles and equations would still remain the same.